# Results of Algebraic and Analytic Methods

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DLMF Formula Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
1.2.E1 ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}=\frac{n!}{(n-k)!k!}}}$ binomial(n,k)=(factorial(n))/(factorial(n - k)*factorial(k)) Binomial[n,k]=Divide[(n)!,(n - k)!*(k)!] Successful Successful - -
1.2.E1 ${\displaystyle{\displaystyle\frac{n!}{(n-k)!k!}=\genfrac{(}{)}{0.0pt}{}{n}{n-k% }}}$ (factorial(n))/(factorial(n - k)*factorial(k))=binomial(n,n - k) Divide[(n)!,(n - k)!*(k)!]=Binomial[n,n - k] Successful Successful - -
1.2.E6 ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{z}{k}=\frac{z(z-1)\cdots(z% -k+1)}{k!}}}$ binomial(z,k)=(z*(z - 1)..(z - k + 1))/(factorial(k)) Binomial[z,k]=Divide[z*(z - 1) ... (z - k + 1),(k)!] Successful Successful - -
1.2.E7 ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{z+1}{k}=\genfrac{(}{)}{0.0% pt}{}{z}{k}+\genfrac{(}{)}{0.0pt}{}{z}{k-1}}}$ binomial(z + 1,k)=binomial(z,k)+binomial(z,k - 1) Binomial[z + 1,k]=Binomial[z,k]+Binomial[z,k - 1] Successful Successful - -
1.2.E8 ${\displaystyle{\displaystyle\sum^{m}_{k=0}\genfrac{(}{)}{0.0pt}{}{z+k}{k}=% \genfrac{(}{)}{0.0pt}{}{z+m+1}{m}}}$ sum(binomial(z + k,k), k = 0..m)=binomial(z + m + 1,m) Sum[Binomial[z + k,k], {k, 0, m}]=Binomial[z + m + 1,m] Successful Successful - -
1.4.E8 ${\displaystyle{\displaystyle f^{(2)}(x)=\frac{{\mathrm{d}}^{2}f}{{\mathrm{d}x}% ^{2}}}}$ (f)^(2)*(x)= diff(f, [x$(2)]) (f)^(2)*(x)= D[f, {x, 2}] Failure Failure Fail 0.+3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), x = 1} 0.+7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), x = 2} 0.+11.99999999*I <- {f = 2^(1/2)+I*2^(1/2), x = 3} 0.-3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), x = 1} 0.-7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), x = 2} 0.-11.99999999*I <- {f = 2^(1/2)-I*2^(1/2), x = 3} 0.+3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), x = 1} 0.+7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), x = 2} 0.+11.99999999*I <- {f = -2^(1/2)-I*2^(1/2), x = 3} 0.-3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), x = 1} 0.-7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), x = 2} 0.-11.99999999*I <- {f = -2^(1/2)+I*2^(1/2), x = 3} Fail Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]} Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]} Complex[0.0, 12.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]} Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]} Complex[0.0, -12.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]} Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1]} Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]} Complex[0.0, 12.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]} Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1]} Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]} Complex[0.0, -12.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]} 1.4.E8 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}f}{{\mathrm{d}x}^{2}}=\frac{% \mathrm{d}}{\mathrm{d}x}\left(\frac{\mathrm{d}f}{\mathrm{d}x}\right)}}$ diff(f, [x$(2)])= diff(diff(f, x), x) D[f, {x, 2}]= D[D[f, x], x] Successful Successful - -
1.4.E9 ${\displaystyle{\displaystyle f^{(n)}=f^{(n)}(x)}}$ (f)^(n)= (f)^(n)*(x) (f)^(n)= (f)^(n)*(x) Failure Failure
Fail
-1.414213562-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}
-2.828427124-2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}
-0.-3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}
-0.-7.999999996*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}
5.656854245-5.656854245*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}
11.31370849-11.31370849*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}
-1.414213562+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}
-2.828427124+2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}
-0.+3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}
-0.+7.999999996*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}
5.656854245+5.656854245*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}
11.31370849+11.31370849*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}
1.414213562+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}
2.828427124+2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}
-0.-3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}
-0.-7.999999996*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}
-5.656854245+5.656854245*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}
-11.31370849+11.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}
1.414213562-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}
2.828427124-2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}
-0.+3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}
-0.+7.999999996*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}
-5.656854245-5.656854245*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}
-11.31370849-11.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3}
Fail
Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}
Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}
Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}
Complex[0.0, -8.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}
Complex[11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}
Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}
Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}
Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}
Complex[0.0, 8.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}
Complex[11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}
Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}
Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}
Complex[0.0, -8.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}
Complex[-11.313708498984761, 11.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}
Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}
Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}
Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}
Complex[0.0, 8.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}
Complex[-11.313708498984761, -11.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}
1.4.E9 ${\displaystyle{\displaystyle f^{(n)}(x)=\frac{\mathrm{d}}{\mathrm{d}x}f^{(n-1)% }(x)}}$ (f)^(n)*(x)= diff((f)^(n - 1)*(x), x) (f)^(n)*(x)= D[(f)^(n - 1)*(x), x] Failure Failure
Fail
.414213562+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 1}
1.828427124+2.828427124*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 2}
3.242640686+4.242640686*I <- {f = 2^(1/2)+I*2^(1/2), n = 1, x = 3}
-1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 1}
-1.414213562+6.585786434*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 2}
-1.414213562+10.58578643*I <- {f = 2^(1/2)+I*2^(1/2), n = 2, x = 3}
-5.656854245+1.656854247*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 1}
-11.31370849+7.313708492*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 2}
-16.97056274+12.97056274*I <- {f = 2^(1/2)+I*2^(1/2), n = 3, x = 3}
.414213562-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 1}
1.828427124-2.828427124*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 2}
3.242640686-4.242640686*I <- {f = 2^(1/2)-I*2^(1/2), n = 1, x = 3}
-1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 1}
-1.414213562-6.585786434*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 2}
-1.414213562-10.58578643*I <- {f = 2^(1/2)-I*2^(1/2), n = 2, x = 3}
-5.656854245-1.656854247*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 1}
-11.31370849-7.313708492*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 2}
-16.97056274-12.97056274*I <- {f = 2^(1/2)-I*2^(1/2), n = 3, x = 3}
-2.414213562-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 1}
-3.828427124-2.828427124*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 2}
-5.242640686-4.242640686*I <- {f = -2^(1/2)-I*2^(1/2), n = 1, x = 3}
1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 1}
1.414213562+9.414213558*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 2}
1.414213562+13.41421355*I <- {f = -2^(1/2)-I*2^(1/2), n = 2, x = 3}
5.656854245-9.656854243*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 1}
11.31370849-15.31370849*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 2}
16.97056274-20.97056274*I <- {f = -2^(1/2)-I*2^(1/2), n = 3, x = 3}
-2.414213562+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 1}
-3.828427124+2.828427124*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 2}
-5.242640686+4.242640686*I <- {f = -2^(1/2)+I*2^(1/2), n = 1, x = 3}
1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 1}
1.414213562-9.414213558*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 2}
1.414213562-13.41421355*I <- {f = -2^(1/2)+I*2^(1/2), n = 2, x = 3}
5.656854245+9.656854243*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 1}
11.31370849+15.31370849*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 2}
16.97056274+20.97056274*I <- {f = -2^(1/2)+I*2^(1/2), n = 3, x = 3}
Fail
Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}
Complex[1.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}
Complex[3.2426406871192857, 4.242640687119286] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}
Complex[-1.4142135623730951, 2.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}
Complex[-1.4142135623730951, 6.585786437626905] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}
Complex[-1.4142135623730951, 10.585786437626904] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}
Complex[-5.656854249492381, 1.6568542494923806] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}
Complex[-11.313708498984761, 7.313708498984761] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}
Complex[-16.970562748477143, 12.970562748477143] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}
Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}
Complex[1.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}
Complex[3.2426406871192857, -4.242640687119286] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}
Complex[-1.4142135623730951, -2.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}
Complex[-1.4142135623730951, -6.585786437626905] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}
Complex[-1.4142135623730951, -10.585786437626904] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}
Complex[-5.656854249492381, -1.6568542494923806] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}
Complex[-11.313708498984761, -7.313708498984761] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}
Complex[-16.970562748477143, -12.970562748477143] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}
Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}
Complex[-3.8284271247461903, -2.8284271247461903] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}
Complex[-5.242640687119286, -4.242640687119286] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}
Complex[1.4142135623730951, 5.414213562373095] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}
Complex[1.4142135623730951, 9.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}
Complex[1.4142135623730951, 13.414213562373096] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}
Complex[5.656854249492381, -9.65685424949238] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}
Complex[11.313708498984761, -15.313708498984761] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}
Complex[16.970562748477143, -20.970562748477143] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}
Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 1]}
Complex[-3.8284271247461903, 2.8284271247461903] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 2]}
Complex[-5.242640687119286, 4.242640687119286] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 1], Rule[x, 3]}
Complex[1.4142135623730951, -5.414213562373095] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 1]}
Complex[1.4142135623730951, -9.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 2]}
Complex[1.4142135623730951, -13.414213562373096] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 2], Rule[x, 3]}
Complex[5.656854249492381, 9.65685424949238] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 1]}
Complex[11.313708498984761, 15.313708498984761] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 2]}
Complex[16.970562748477143, 20.970562748477143] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[n, 3], Rule[x, 3]}
1.4.E16 ${\displaystyle{\displaystyle\int fg\mathrm{d}x=\left(\int f\mathrm{d}x\right)g% -\int\left(\int f\mathrm{d}x\right)\frac{\mathrm{d}g}{\mathrm{d}x}\mathrm{d}x}}$ int(f*g, x)=(int(f, x))* g - int((int(f, x))* diff(g, x), x) Integrate[f*g, x]=(Integrate[f, x])* g - Integrate[(Integrate[f, x])* D[g, x], x] Successful Successful - -
1.4.E37 ${\displaystyle{\displaystyle R_{n}=\frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(% t)\mathrm{d}t}}$ R[n]=(1)/(factorial(n))*int((x - t)^(n)* (f)^(n + 1)*(t), t = a..x) Subscript[R, n]=Divide[1,(n)!]*Integrate[(x - t)^(n)* (f)^(n + 1)*(t), {t, a, x}] Failure Failure Skip Skip
1.5.E4 ${\displaystyle{\displaystyle\frac{\partial f}{\partial y}=D_{y}f}}$ diff(f, y)= D[y]*f D[f, y]= Subscript[D, y]*f Failure Failure
Fail
-0.-3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}
-3.999999998-0.*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}
-0.+3.999999998*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}
3.999999998-0.*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}
-3.999999998-0.*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}
-0.+3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}
3.999999998-0.*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}
-0.-3.999999998*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}
-0.+3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}
3.999999998-0.*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}
-0.-3.999999998*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}
-3.999999998-0.*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}
3.999999998-0.*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2)}
-0.-3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2)}
-3.999999998-0.*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2)}
-0.+3.999999998*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2)}
Fail
Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-4.0 <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
4.0 <- {Rule[f, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
-4.0 <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
4.0 <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -4.0] <- {Rule[f, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
4.0 <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-4.0 <- {Rule[f, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
4.0 <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-4.0 <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 4.0] <- {Rule[f, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[D, y], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5.E4 ${\displaystyle{\displaystyle D_{y}f=f_{y}}}$ D[y]*f = f[y] Subscript[D, y]*f = Subscript[f, y] Failure Failure
Fail
-1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-1.414213562+5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
1.414213562+5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
1.414213562+2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
2.585786436-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
2.585786436+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
5.414213560+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
5.414213560-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-1.414213562-5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-1.414213562-2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
1.414213562-2.585786436*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
1.414213562-5.414213560*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-5.414213560-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-5.414213560+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
-2.585786436+1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
-2.585786436-1.414213562*I <- {f = 2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
2.585786436-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
2.585786436+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
5.414213560+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
5.414213560-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-1.414213562-5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
1.414213562-2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
1.414213562-5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-5.414213560-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-5.414213560+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
-2.585786436+1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
-2.585786436-1.414213562*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-1.414213562+2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-1.414213562+5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
1.414213562+5.414213560*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
1.414213562+2.585786436*I <- {f = 2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-1.414213562-5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-1.414213562-2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
1.414213562-2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
1.414213562-5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-5.414213560-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-5.414213560+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
-2.585786436+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
-2.585786436-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-1.414213562+2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
1.414213562+5.414213560*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
1.414213562+2.585786436*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
2.585786436-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
2.585786436+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
5.414213560+1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
5.414213560-1.414213562*I <- {f = -2^(1/2)-I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-5.414213560-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-5.414213560+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
-2.585786436+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
-2.585786436-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-1.414213562+2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-1.414213562+5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
1.414213562+5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
1.414213562+2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = 2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
2.585786436-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
2.585786436+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
5.414213560+1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
5.414213560-1.414213562*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)-I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
-1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)+I*2^(1/2)}
-1.414213562-2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = 2^(1/2)-I*2^(1/2)}
1.414213562-2.585786436*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)-I*2^(1/2)}
1.414213562-5.414213560*I <- {f = -2^(1/2)+I*2^(1/2), D[y] = -2^(1/2)+I*2^(1/2), f[y] = -2^(1/2)+I*2^(1/2)}
Successful
1.5#Ex3 ${\displaystyle{\displaystyle x=r\cos\phi}}$ x = r*cos(phi) x = r*Cos[\[Phi]] Failure Failure
Fail
-2.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}
-1.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}
-.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}
3.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}
4.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}
5.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}
4.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}
5.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}
6.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}
-1.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}
-.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}
.777253510-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}
3.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}
4.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}
5.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}
-2.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}
-1.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}
-.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}
-1.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}
-.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}
.777253510+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}
4.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}
5.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}
6.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}
-2.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}
-1.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}
-.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}
3.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}
4.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}
5.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}
4.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}
5.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}
6.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}
-1.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}
-.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}
.777253510-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}
3.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}
4.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}
5.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}
-2.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}
-1.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}
-.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}
-1.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}
-.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}
.777253510+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}
4.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}
5.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}
6.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}
Fail
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex4 ${\displaystyle{\displaystyle y=r\sin\phi}}$ y = r*sin(phi) y = r*Sin[\[Phi]] Failure Failure
Fail
-1.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}
-.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}
.384024424-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}
-2.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}
-1.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}
-.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}
3.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}
4.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}
5.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}
4.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}
5.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}
6.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}
-2.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}
-1.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}
-.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}
-1.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}
-.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}
.384024424+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}
4.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}
5.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}
6.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}
3.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}
4.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}
5.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}
3.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}
4.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}
5.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}
4.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}
5.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}
6.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}
-1.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}
-.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}
.384024424-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}
-2.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}
-1.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}
-.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}
4.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}
5.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}
6.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}
3.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}
4.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}
5.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}
-2.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}
-1.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}
-.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}
-1.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}
-.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}
.384024424+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}
Fail
Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5.E13 ${\displaystyle{\displaystyle\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{% \partial}^{2}f}{{\partial y}^{2}}=\frac{{\partial}^{2}f}{{\partial r}^{2}}+% \frac{1}{r}\frac{\partial f}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}f}% {{\partial\phi}^{2}}}}$ diff(f, [x$(2)])+ diff(f, [y$(2)])= diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)]) D[f, {x, 2}]+ D[f, {y, 2}]= D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}] Successful Successful - -
1.5#Ex5 ${\displaystyle{\displaystyle x=r\cos\phi}}$ x = r*cos(phi) x = r*Cos[\[Phi]] Failure Failure
Fail
-2.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}
-1.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}
-.183489624+2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}
3.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}
4.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}
5.222746490+3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}
4.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}
5.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}
6.183489624-2.222746490*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}
-1.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}
-.222746490-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}
.777253510-3.183489624*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}
3.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}
4.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}
5.222746490-3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}
-2.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}
-1.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}
-.183489624-2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}
-1.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}
-.222746490+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}
.777253510+3.183489624*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}
4.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}
5.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}
6.183489624+2.222746490*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}
-2.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}
-1.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}
-.183489624+2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}
3.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}
4.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}
5.222746490+3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}
4.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}
5.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}
6.183489624-2.222746490*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}
-1.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}
-.222746490-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}
.777253510-3.183489624*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}
3.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 1}
4.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 2}
5.222746490-3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), x = 3}
-2.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 1}
-1.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 2}
-.183489624-2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), x = 3}
-1.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 1}
-.222746490+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 2}
.777253510+3.183489624*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), x = 3}
4.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 1}
5.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 2}
6.183489624+2.222746490*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), x = 3}
Fail
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex6 ${\displaystyle{\displaystyle y=r\sin\phi}}$ y = r*sin(phi) y = r*Sin[\[Phi]] Failure Failure
Fail
-1.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}
-.615975576-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}
.384024424-3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}
-2.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}
-1.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}
-.469485904+2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}
3.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}
4.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}
5.615975576+3.469485904*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}
4.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}
5.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}
6.469485904-2.615975576*I <- {phi = 2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}
-2.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}
-1.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}
-.469485904-2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}
-1.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}
-.615975576+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}
.384024424+3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}
4.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}
5.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}
6.469485904+2.615975576*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}
3.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}
4.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}
5.615975576-3.469485904*I <- {phi = 2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}
3.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}
4.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}
5.615975576+3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}
4.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}
5.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}
6.469485904-2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}
-1.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}
-.615975576-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}
.384024424-3.469485904*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}
-2.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}
-1.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}
-.469485904+2.615975576*I <- {phi = -2^(1/2)-I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}
4.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 1}
5.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 2}
6.469485904+2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)+I*2^(1/2), y = 3}
3.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 1}
4.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 2}
5.615975576-3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = 2^(1/2)-I*2^(1/2), y = 3}
-2.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 1}
-1.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 2}
-.469485904-2.615975576*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)-I*2^(1/2), y = 3}
-1.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 1}
-.615975576+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 2}
.384024424+3.469485904*I <- {phi = -2^(1/2)+I*2^(1/2), r = -2^(1/2)+I*2^(1/2), y = 3}
Fail
Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex8 ${\displaystyle{\displaystyle x=\rho\sin\theta\cos\phi}}$ x = rho*sin(theta)*cos(phi) x = \[Rho]*Sin[\[Theta]]*Cos[\[Phi]] Failure Failure
Fail
-6.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-5.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
-4.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-5.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-4.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
-3.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
8.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
9.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
10.52013032-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
7.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
8.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
9.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
4.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
5.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
6.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
6.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
7.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
8.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-2.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-1.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
-.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-4.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-3.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
-2.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
8.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
9.520130316-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
10.52013032-3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
7.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
8.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
9.178651817-5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-6.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-5.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
-4.520130316+3.821663559*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-5.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-4.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
-3.178651817+5.742972580*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
-2.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-1.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
-.821663559-7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-4.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-3.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
-2.742972580-6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
4.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
5.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
6.821663559+7.520130316*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
6.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
7.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
8.742972580+6.178651817*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
6.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
7.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
8.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
4.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
5.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
6.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-4.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-3.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
-2.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-2.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-1.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
-.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
-5.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-4.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
-3.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-6.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-5.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
-4.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
7.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
8.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
9.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
8.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
9.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
10.52013032+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
-4.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-3.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
-2.742972580+6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-2.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-1.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
-.821663559+7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
6.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
7.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
8.742972580-6.178651817*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
4.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
5.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
6.821663559-7.520130316*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
7.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
8.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
9.178651817+5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
8.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
9.520130316+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
10.52013032+3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-5.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-4.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
-3.178651817-5.742972580*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-6.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-5.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
-4.520130316-3.821663559*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
-6.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-5.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
-4.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-5.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-4.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
-3.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
8.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
9.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
10.52013032-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
7.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
8.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
9.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
4.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
5.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
6.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
6.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
7.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
8.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-2.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-1.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
-.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-4.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-3.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
-2.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
8.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
9.520130316-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
10.52013032-3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
7.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
8.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
9.178651817-5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-6.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-5.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
-4.520130316+3.821663559*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-5.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-4.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
-3.178651817+5.742972580*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
-2.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-1.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
-.821663559-7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-4.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-3.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
-2.742972580-6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
4.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
5.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
6.821663559+7.520130316*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
6.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
7.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
8.742972580+6.178651817*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
6.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
7.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
8.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
4.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
5.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
6.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-4.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-3.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
-2.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-2.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-1.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
-.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
-5.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-4.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
-3.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-6.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-5.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
-4.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
7.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
8.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
9.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
8.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
9.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
10.52013032+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
-4.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-3.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
-2.742972580+6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-2.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-1.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
-.821663559+7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
6.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
7.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
8.742972580-6.178651817*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
4.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
5.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
6.821663559-7.520130316*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
7.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
8.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
9.178651817+5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
8.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
9.520130316+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
10.52013032+3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-5.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-4.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
-3.178651817-5.742972580*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-6.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-5.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
-4.520130316-3.821663559*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
Fail
Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.178651825187201, -5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.1786518251872, -5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.1786518251872, -5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.821663571698538, 7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.8216635716985379, 7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.8216635716985379, 7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.742972588953473, -6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.7429725889534726, -6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.7429725889534726, -6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.520130323279806, 3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.520130323279806, 3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.520130323279806, 3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.178651825187201, 5.742972588953473] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.178651825187201, 5.742972588953473] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.1786518251872007, 5.742972588953473] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.821663571698538, -7.5201303232798065] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.821663571698538, -7.5201303232798065] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.821663571698538, -7.5201303232798065] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.742972588953473, 6.178651825187201] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.742972588953473, 6.178651825187201] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.742972588953473, 6.178651825187201] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.5201303232798065, -3.821663571698538] <- {Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.5201303232798065, -3.821663571698538] <- {Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.5201303232798065, -3.821663571698538] <- {Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex9 ${\displaystyle{\displaystyle y=\rho\sin\theta\sin\phi}}$ y = rho*sin(theta)*sin(phi) y = \[Rho]*Sin[\[Theta]]*Sin[\[Phi]] Failure Failure
Fail
-3.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-2.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
-1.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-5.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-4.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
-3.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
5.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
6.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
7.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
7.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
8.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
9.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
-7.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-6.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
-5.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-5.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-4.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
-3.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
9.254122865-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
10.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
11.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
7.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
8.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
9.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
5.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
6.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
7.581407255+8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
7.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
8.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
9.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-3.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-2.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
-1.581407255-8.254122865*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-5.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-4.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
-3.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
9.254122865-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
10.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
11.25412286-4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
7.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
8.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
9.675321591-6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-7.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-6.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
-5.254122865+4.581407255*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-5.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-4.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
-3.675321591+6.675321591*I <- {phi = 2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
-5.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-4.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
-3.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-7.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-6.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
-5.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
7.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
8.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
9.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
9.254122865+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
10.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
11.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
-5.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-4.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
-3.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-3.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-2.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
-1.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
7.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
8.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
9.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
5.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
6.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
7.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
7.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
8.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
9.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
9.254122865+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
10.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
11.25412286+4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-5.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-4.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
-3.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-7.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-6.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
-5.254122865-4.581407255*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
7.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
8.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
9.675321591-6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
5.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
6.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
7.581407255-8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-5.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-4.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
-3.675321591+6.675321591*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-3.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-2.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
-1.581407255+8.254122865*I <- {phi = 2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
5.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
6.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
7.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
7.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
8.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
9.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-3.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-2.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
-1.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-5.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-4.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
-3.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
9.254122865-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
10.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
11.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
7.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
8.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
9.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-7.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-6.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
-5.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-5.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-4.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
-3.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
-3.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-2.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
-1.581407255-8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-5.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-4.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
-3.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
5.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
6.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
7.581407255+8.254122865*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
7.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
8.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
9.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
-7.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-6.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
-5.254122865+4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-5.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-4.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
-3.675321591+6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
9.254122865-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
10.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
11.25412286-4.581407255*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
7.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
8.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
9.675321591-6.675321591*I <- {phi = -2^(1/2)-I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
7.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
8.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
9.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
9.254122865+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
10.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
11.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-5.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-4.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
-3.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-7.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-6.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
-5.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
7.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
8.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
9.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
5.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
6.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
7.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-5.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-4.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
-3.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-3.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-2.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
-1.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
-5.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-4.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
-3.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-7.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-6.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
-5.254122865-4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
7.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
8.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
9.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
9.254122865+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
10.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
11.25412286+4.581407255*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
-5.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-4.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
-3.675321591+6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-3.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-2.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
-1.581407255+8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
7.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
8.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
9.675321591-6.675321591*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
5.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
6.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
7.581407255-8.254122865*I <- {phi = -2^(1/2)+I*2^(1/2), rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
Fail
Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-7.254122872375824, -4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.254122872375824, -4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.254122872375824, -4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.254122872375824, 4.5814072673136925] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[10.254122872375824, 4.5814072673136925] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.254122872375824, 4.5814072673136925] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.6753216005400215, 6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.6753216005400215, 6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.6753216005400215, 6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.5814072673136925, 8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5814072673136925, 8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5814072673136925, 8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[7.6753216005400215, -6.6753216005400215] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[8.675321600540022, -6.6753216005400215] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[9.675321600540022, -6.6753216005400215] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.5814072673136925, -8.254122872375824] <- {Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.5814072673136925, -8.254122872375824] <- {Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.5814072673136925, -8.254122872375824] <- {Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ϕ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5#Ex10 ${\displaystyle{\displaystyle z=\rho\cos\theta}}$ z = rho*cos(theta) z = \[Rho]*Cos[\[Theta]] Failure Failure
Fail
-1.769276062+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-1.769276062+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-4.597703186+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-4.597703186+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
3.636960052-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
3.636960052-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
.808532928-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
.808532928-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-1.769276062+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-1.769276062+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-4.597703186+.808532928*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-4.597703186+3.636960052*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
3.636960052-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
3.636960052-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
.808532928-4.597703186*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
.808532928-1.769276062*I <- {rho = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
3.636960052+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
3.636960052+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
.808532928+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
.808532928+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-1.769276062-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-1.769276062-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-4.597703186-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-4.597703186-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
3.636960052+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
3.636960052+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
.808532928+1.769276062*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
.808532928+4.597703186*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-1.769276062-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-1.769276062-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-4.597703186-3.636960052*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-4.597703186-.808532928*I <- {rho = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
4.597703186-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
4.597703186-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
1.769276062-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
1.769276062-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-.808532928+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-.808532928+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-3.636960052+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-3.636960052+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
4.597703186-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
4.597703186-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
1.769276062-3.636960052*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
1.769276062-.808532928*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-.808532928+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-.808532928+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-3.636960052+1.769276062*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-3.636960052+4.597703186*I <- {rho = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-.808532928-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-.808532928-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-3.636960052-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-3.636960052-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
4.597703186+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
4.597703186+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
1.769276062+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
1.769276062+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-.808532928-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-.808532928-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-3.636960052-4.597703186*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-3.636960052-1.769276062*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
4.597703186+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
4.597703186+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
1.769276062+.808532928*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
1.769276062+3.636960052*I <- {rho = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[-1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.597703187633898, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.8085329312075371, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.7692760628877078, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.636960055953727, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.8085329312075371, -4.597703187633898] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.597703187633898, -3.636960055953727] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.636960055953727, 1.7692760628877078] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.7692760628877078, 0.8085329312075371] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.597703187633898, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.8085329312075371, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.7692760628877078, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.636960055953727, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.8085329312075371, -1.7692760628877078] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.597703187633898, -0.8085329312075371] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.636960055953727, 4.597703187633898] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.7692760628877078, 3.636960055953727] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ρ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.5.E17 ${\displaystyle{\displaystyle\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{% \partial}^{2}f}{{\partial y}^{2}}+\frac{{\partial}^{2}f}{{\partial z}^{2}}={% \frac{1}{\rho^{2}}\frac{\partial}{\partial\rho}\left(\rho^{2}\frac{\partial f}% {\partial\rho}\right)+\frac{1}{\rho^{2}{\sin^{2}}\theta}\frac{{\partial}^{2}f}% {{\partial\phi}^{2}}}+\frac{1}{\rho^{2}\sin\theta}\frac{\partial}{\partial% \theta}\left(\sin\theta\frac{\partial f}{\partial\theta}\right)}}$ diff(f, [x$(2)])+ diff(f, [y$(2)])+ diff(f, [z$(2)])=(1)/((rho)^(2))*diff(((rho)^(2)* diff(f, rho))+(1)/((rho)^(2)* (sin(theta))^(2))*diff(f, [phi$(2)]), rho)+(1)/((rho)^(2)* sin(theta))*diff(sin(theta)*diff(f, theta), theta) D[f, {x, 2}]+ D[f, {y, 2}]+ D[f, {z, 2}]=Divide[1,(\[Rho])^(2)]*D[((\[Rho])^(2)* D[f, \[Rho]])+Divide[1,(\[Rho])^(2)* (Sin[\[Theta]])^(2)]*D[f, {\[Phi], 2}], \[Rho]]+Divide[1,(\[Rho])^(2)* Sin[\[Theta]]]*D[Sin[\[Theta]]*D[f, \[Theta]], \[Theta]] Successful Successful - -
1.5.E19 ${\displaystyle{\displaystyle\frac{\partial f}{\partial x}=\frac{\partial f}{% \partial y}}}$ diff(f, x)= diff(f, y) D[f, x]= D[f, y] Successful Successful - -
1.5.E23 ${\displaystyle{\displaystyle\left|\int_{c_{1}}^{d}(\ifrac{\partial f}{\partial x% })\mathrm{d}y\right|<\epsilon}}$ abs(int(diff(f, x), y = c[1]..d))< epsilon Abs[Integrate[D[f, x], {y, Subscript[c, 1], d}]]< \[Epsilon] Failure Failure Skip Successful
1.6#Ex15 ${\displaystyle{\displaystyle\epsilon_{123}=\epsilon_{312}}}$ LeviCivita[1, 2, 3]= LeviCivita[3, 1, 2] Part[LeviCivitaTensor[3,List], 1, 2, 3]= Part[LeviCivitaTensor[3,List], 3, 1, 2] Failure Successful
Fail
2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}
2.828427124+2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}
2.828427124 <- {LeviCivita[1,2,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}
-2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}
2.828427124 <- {LeviCivita[1,2,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}
2.828427124-2.828427124*I <- {LeviCivita[1,2,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}
-2.828427124-2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}
-2.828427124 <- {LeviCivita[1,2,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}
-2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}
-2.828427124 <- {LeviCivita[1,2,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}
-2.828427124+2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}
2.828427124*I <- {LeviCivita[1,2,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}
-
1.6#Ex15 ${\displaystyle{\displaystyle\epsilon_{312}=1}}$ LeviCivita[3, 1, 2]= 1 Part[LeviCivitaTensor[3,List], 3, 1, 2]= 1 Failure Successful
Fail
.414213562+1.414213562*I <- {LeviCivita[3,1,2] = 2^(1/2)+I*2^(1/2)}
.414213562-1.414213562*I <- {LeviCivita[3,1,2] = 2^(1/2)-I*2^(1/2)}
-2.414213562-1.414213562*I <- {LeviCivita[3,1,2] = -2^(1/2)-I*2^(1/2)}
-2.414213562+1.414213562*I <- {LeviCivita[3,1,2] = -2^(1/2)+I*2^(1/2)}
-
1.6#Ex16 ${\displaystyle{\displaystyle\epsilon_{213}=\epsilon_{321}}}$ LeviCivita[2, 1, 3]= LeviCivita[3, 2, 1] Part[LeviCivitaTensor[3,List], 2, 1, 3]= Part[LeviCivitaTensor[3,List], 3, 2, 1] Failure Successful
Fail
2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}
2.828427124+2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}
2.828427124 <- {LeviCivita[2,1,3] = 2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}
-2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}
2.828427124 <- {LeviCivita[2,1,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}
2.828427124-2.828427124*I <- {LeviCivita[2,1,3] = 2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}
-2.828427124-2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}
-2.828427124 <- {LeviCivita[2,1,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}
-2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)-I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}
-2.828427124 <- {LeviCivita[2,1,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}
-2.828427124+2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}
2.828427124*I <- {LeviCivita[2,1,3] = -2^(1/2)+I*2^(1/2), LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}
-
1.6#Ex16 ${\displaystyle{\displaystyle\epsilon_{321}=-1}}$ LeviCivita[3, 2, 1]= - 1 Part[LeviCivitaTensor[3,List], 3, 2, 1]= - 1 Failure Successful
Fail
2.414213562+1.414213562*I <- {LeviCivita[3,2,1] = 2^(1/2)+I*2^(1/2)}
2.414213562-1.414213562*I <- {LeviCivita[3,2,1] = 2^(1/2)-I*2^(1/2)}
-.414213562-1.414213562*I <- {LeviCivita[3,2,1] = -2^(1/2)-I*2^(1/2)}
-.414213562+1.414213562*I <- {LeviCivita[3,2,1] = -2^(1/2)+I*2^(1/2)}
-
1.6#Ex17 ${\displaystyle{\displaystyle\epsilon_{221}=0}}$ LeviCivita[2, 2, 1]= 0 Part[LeviCivitaTensor[3,List], 2, 2, 1]= 0 Failure Successful
Fail
1.414213562+1.414213562*I <- {LeviCivita[2,2,1] = 2^(1/2)+I*2^(1/2)}
1.414213562-1.414213562*I <- {LeviCivita[2,2,1] = 2^(1/2)-I*2^(1/2)}
-1.414213562-1.414213562*I <- {LeviCivita[2,2,1] = -2^(1/2)-I*2^(1/2)}
-1.414213562+1.414213562*I <- {LeviCivita[2,2,1] = -2^(1/2)+I*2^(1/2)}
-
1.6.E16 ${\displaystyle{\displaystyle\epsilon_{jk\ell}\epsilon_{\ell mn}=\delta_{j,m}% \delta_{k,n}-\delta_{j,n}\delta_{k,m}}}$ LeviCivita[j, k, ell]*LeviCivita[ell, m, n]= KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m] Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Part[LeviCivitaTensor[3,List], \[ScriptL], m, n]= KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m] Failure Failure Skip Successful
1.6.E46 ${\displaystyle{\displaystyle\mathbf{T}_{u}=\frac{\partial x}{\partial u}(u_{0}% ,v_{0})\mathbf{i}+\frac{\partial y}{\partial u}(u_{0},v_{0})\mathbf{j}+\frac{% \partial z}{\partial u}(u_{0},v_{0})\mathbf{k}}}$ T[u]= diff(x, u)*(u[0], v[0])* I + diff(y, u)*(u[0], v[0])* j + diff(z, u)*(u[0], v[0])* k Subscript[T, u]= D[x, u]*(Subscript[u, 0], Subscript[v, 0])* I + D[y, u]*(Subscript[u, 0], Subscript[v, 0])* j + D[z, u]*(Subscript[u, 0], Subscript[v, 0])* k Failure Failure
Fail
1.414213562+1.414213562*I <- {T[u] = 2^(1/2)+I*2^(1/2)}
1.414213562-1.414213562*I <- {T[u] = 2^(1/2)-I*2^(1/2)}
-1.414213562-1.414213562*I <- {T[u] = -2^(1/2)-I*2^(1/2)}
-1.414213562+1.414213562*I <- {T[u] = -2^(1/2)+I*2^(1/2)}
Error
1.6.E47 ${\displaystyle{\displaystyle\mathbf{T}_{v}=\frac{\partial x}{\partial v}(u_{0}% ,v_{0})\mathbf{i}+\frac{\partial y}{\partial v}(u_{0},v_{0})\mathbf{j}+\frac{% \partial z}{\partial v}(u_{0},v_{0})\mathbf{k}}}$ T[v]= diff(x, v)*(u[0], v[0])* I + diff(y, v)*(u[0], v[0])* j + diff(z, v)*(u[0], v[0])* k Subscript[T, v]= D[x, v]*(Subscript[u, 0], Subscript[v, 0])* I + D[y, v]*(Subscript[u, 0], Subscript[v, 0])* j + D[z, v]*(Subscript[u, 0], Subscript[v, 0])* k Failure Failure
Fail
1.414213562+1.414213562*I <- {T[v] = 2^(1/2)+I*2^(1/2)}
1.414213562-1.414213562*I <- {T[v] = 2^(1/2)-I*2^(1/2)}
-1.414213562-1.414213562*I <- {T[v] = -2^(1/2)-I*2^(1/2)}
-1.414213562+1.414213562*I <- {T[v] = -2^(1/2)+I*2^(1/2)}
Error
1.8.E16 ${\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega}={% \sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega% }\cos\left(2n\pi x\right)\right)}}}$ sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity)=sqrt((Pi)/(omega))*(1 + 2*sum(exp(- (n)^(2)* (Pi)^(2)/ omega)*cos(2*n*Pi*x), n = 1..infinity)) Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}]=Sqrt[Divide[Pi,\[Omega]]]*(1 + 2*Sum[Exp[- (n)^(2)* (Pi)^(2)/ \[Omega]]*Cos[2*n*Pi*x], {n, 1, Infinity}]) Failure Successful Skip -
1.9#Ex1 ${\displaystyle{\displaystyle\Re z=x}}$ Re(z)= x Re[z]= x Failure Failure
Fail
.414213562 <- {z = 2^(1/2)+I*2^(1/2), x = 1}
-.585786438 <- {z = 2^(1/2)+I*2^(1/2), x = 2}
-1.585786438 <- {z = 2^(1/2)+I*2^(1/2), x = 3}
.414213562 <- {z = 2^(1/2)-I*2^(1/2), x = 1}
-.585786438 <- {z = 2^(1/2)-I*2^(1/2), x = 2}
-1.585786438 <- {z = 2^(1/2)-I*2^(1/2), x = 3}
-2.414213562 <- {z = -2^(1/2)-I*2^(1/2), x = 1}
-3.414213562 <- {z = -2^(1/2)-I*2^(1/2), x = 2}
-4.414213562 <- {z = -2^(1/2)-I*2^(1/2), x = 3}
-2.414213562 <- {z = -2^(1/2)+I*2^(1/2), x = 1}
-3.414213562 <- {z = -2^(1/2)+I*2^(1/2), x = 2}
-4.414213562 <- {z = -2^(1/2)+I*2^(1/2), x = 3}
Fail
0.41421356237309515 <- {Rule[x, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-0.5857864376269049 <- {Rule[x, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-1.5857864376269049 <- {Rule[x, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
0.41421356237309515 <- {Rule[x, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-0.5857864376269049 <- {Rule[x, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-1.5857864376269049 <- {Rule[x, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-2.414213562373095 <- {Rule[x, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-3.414213562373095 <- {Rule[x, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-4.414213562373095 <- {Rule[x, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-2.414213562373095 <- {Rule[x, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
-3.414213562373095 <- {Rule[x, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
-4.414213562373095 <- {Rule[x, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9#Ex2 ${\displaystyle{\displaystyle\Im z=y}}$ Im(z)= y Im[z]= y Failure Failure
Fail
.414213562 <- {z = 2^(1/2)+I*2^(1/2), y = 1}
-.585786438 <- {z = 2^(1/2)+I*2^(1/2), y = 2}
-1.585786438 <- {z = 2^(1/2)+I*2^(1/2), y = 3}
-2.414213562 <- {z = 2^(1/2)-I*2^(1/2), y = 1}
-3.414213562 <- {z = 2^(1/2)-I*2^(1/2), y = 2}
-4.414213562 <- {z = 2^(1/2)-I*2^(1/2), y = 3}
-2.414213562 <- {z = -2^(1/2)-I*2^(1/2), y = 1}
-3.414213562 <- {z = -2^(1/2)-I*2^(1/2), y = 2}
-4.414213562 <- {z = -2^(1/2)-I*2^(1/2), y = 3}
.414213562 <- {z = -2^(1/2)+I*2^(1/2), y = 1}
-.585786438 <- {z = -2^(1/2)+I*2^(1/2), y = 2}
-1.585786438 <- {z = -2^(1/2)+I*2^(1/2), y = 3}
Fail
0.41421356237309515 <- {Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-0.5857864376269049 <- {Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-1.5857864376269049 <- {Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-2.414213562373095 <- {Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-3.414213562373095 <- {Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-4.414213562373095 <- {Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-2.414213562373095 <- {Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-3.414213562373095 <- {Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-4.414213562373095 <- {Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
0.41421356237309515 <- {Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
-0.5857864376269049 <- {Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
-1.5857864376269049 <- {Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9#Ex3 ${\displaystyle{\displaystyle x=r\cos\theta}}$ x = r*cos(theta) x = r*Cos[\[Theta]] Failure Failure
Fail
-2.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-1.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
-.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
3.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
4.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
5.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-2.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-1.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
-.183489624+2.222746490*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
3.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
4.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
5.222746490-3.183489624*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
3.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
4.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
5.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-2.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-1.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
-.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
3.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
4.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
5.222746490+3.183489624*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-2.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-1.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
-.183489624-2.222746490*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
4.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
5.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
6.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
-1.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
-.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
.777253510+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
4.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
5.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
6.183489624-2.222746490*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
-1.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
-.222746490+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
.777253510+3.183489624*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
-1.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 1}
-.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 2}
.777253510-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), x = 3}
4.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 1}
5.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 2}
6.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), x = 3}
-1.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 1}
-.222746490-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 2}
.777253510-3.183489624*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), x = 3}
4.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 1}
5.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 2}
6.183489624+2.222746490*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), x = 3}
Fail
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, 2.2227464935806323] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, -3.183489625260803] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.222746493580632, 3.183489625260803] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.18348962526080292, -2.2227464935806323] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, -2.2227464935806323] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, 3.183489625260803] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.2227464935806323, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.22274649358063225, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.7772535064193677, -3.183489625260803] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.183489625260803, 2.2227464935806323] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9#Ex4 ${\displaystyle{\displaystyle y=r\sin\theta}}$ y = r*sin(theta) y = r*Sin[\[Theta]] Failure Failure
Fail
-1.615975576-3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-.615975576-3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
.384024424-3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-2.469485904-2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-1.469485904-2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
-.469485904-2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
3.615975576+3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
4.615975576+3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
5.615975576+3.469485904*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
4.469485904+2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
5.469485904+2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
6.469485904+2.615975576*I <- {r = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
-2.469485904+2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
-1.469485904+2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
-.469485904+2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
-1.615975576+3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
-.615975576+3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
.384024424+3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
4.469485904-2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
5.469485904-2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
6.469485904-2.615975576*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
3.615975576-3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
4.615975576-3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
5.615975576-3.469485904*I <- {r = 2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
3.615975576+3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
4.615975576+3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
5.615975576+3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
4.469485904+2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
5.469485904+2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
6.469485904+2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-1.615975576-3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-.615975576-3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
.384024424-3.469485904*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-2.469485904-2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-1.469485904-2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
-.469485904-2.615975576*I <- {r = -2^(1/2)-I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
4.469485904-2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 1}
5.469485904-2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 2}
6.469485904-2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2), y = 3}
3.615975576-3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 1}
4.615975576-3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 2}
5.615975576-3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2), y = 3}
-2.469485904+2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 1}
-1.469485904+2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 2}
-.469485904+2.615975576*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2), y = 3}
-1.615975576+3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 1}
-.615975576+3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 2}
.384024424+3.469485904*I <- {r = -2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2), y = 3}
Fail
Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.469485905778385, -2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.6159755792011303, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.61597557920113, -3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4694859057783853, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.46948590577838534, 2.6159755792011303] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 1], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.6159755792011303, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 2], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.38402442079886967, 3.4694859057783853] <- {Rule[r, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[y, 3], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9.E6 ${\displaystyle{\displaystyle\omega=\operatorname{arctan}\left(|y/x|\right)\in% \left[0,\tfrac{1}{2}\pi\right]}}$ omega = arctan(abs(y/ x))in[0 ,(1)/(2)*Pi] \[Omega]= ArcTan[Abs[y/ x]]\[Element][0 ,Divide[1,2]*Pi] Failure Failure Error Error
1.9#Ex6 ${\displaystyle{\displaystyle\operatorname{ph}z=\theta+2n\pi}}$ argument(z)= theta + 2*n*Pi Arg[z]= \[Theta]+ 2*n*Pi Failure Failure
Fail
-6.912000706-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
-13.19518602-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
-19.47837132-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
-8.482797034-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
-14.76598234-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}
-21.04916764-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}
-10.05359336-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}
-16.33677867-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}
-22.61996397-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}
-5.341204380-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}
-11.62438969-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}
-17.90757499-1.414213562*I <- {theta = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}
-6.912000706+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
-13.19518602+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
-19.47837132+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
-8.482797034+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
-14.76598234+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}
-21.04916764+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}
-10.05359336+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}
-16.33677867+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}
-22.61996397+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}
-5.341204380+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}
-11.62438969+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}
-17.90757499+1.414213562*I <- {theta = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}
-4.083573582+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
-10.36675890+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
-16.64994420+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
-5.654369910+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
-11.93755522+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}
-18.22074052+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}
-7.225166236+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}
-13.50835155+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}
-19.79153685+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}
-2.512777256+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}
-8.795962568+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}
-15.07914787+1.414213562*I <- {theta = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}
-4.083573582-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 1}
-10.36675890-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 2}
-16.64994420-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), n = 3}
-5.654369910-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 1}
-11.93755522-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 2}
-18.22074052-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), n = 3}
-7.225166236-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 1}
-13.50835155-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 2}
-19.79153685-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), n = 3}
-2.512777256-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 1}
-8.795962568-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 2}
-15.07914787-1.414213562*I <- {theta = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), n = 3}
Fail
Complex[-6.912000706155233, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-13.195186013334819, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-19.478371320514405, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.912000706155233, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-13.195186013334819, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-19.478371320514405, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.083573581409043, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-10.366758888588627, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-16.649944195768214, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.083573581409043, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-10.366758888588627, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-16.649944195768214, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-8.48279703295013, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-14.765982340129717, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-21.049167647309304, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-8.48279703295013, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-14.765982340129717, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-21.049167647309304, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.65436990820394, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-11.937555215383526, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-18.220740522563112, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.65436990820394, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-11.937555215383526, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-18.220740522563112, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-10.053593359745026, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-16.336778666924612, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-22.6199639741042, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-10.053593359745026, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-16.336778666924612, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-22.6199639741042, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.225166234998835, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-13.50835154217842, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-19.791536849358007, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.225166234998835, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-13.50835154217842, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-19.791536849358007, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.341204379360336, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-11.624389686539924, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-17.90757499371951, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.341204379360336, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-11.624389686539924, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-17.90757499371951, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5127772546141465, 1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-8.795962561793733, 1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-15.079147868973319, 1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.5127772546141465, -1.4142135623730951] <- {Rule[n, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-8.795962561793733, -1.4142135623730951] <- {Rule[n, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-15.079147868973319, -1.4142135623730951] <- {Rule[n, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[θ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9#Ex7 ${\displaystyle{\displaystyle|\Re z|<=|z|}}$ abs(Re(z))< =abs(z) Abs[Re[z]]< =Abs[z] Failure Failure Successful Successful
1.9#Ex8 ${\displaystyle{\displaystyle|\Im z|<=|z|}}$ abs(Im(z))< =abs(z) Abs[Im[z]]< =Abs[z] Failure Failure Successful Successful
1.9.E10 ${\displaystyle{\displaystyle e^{i\theta}=\cos\theta+i\sin\theta}}$ exp(I*theta)= cos(theta)+ I*sin(theta) Exp[I*\[Theta]]= Cos[\[Theta]]+ I*Sin[\[Theta]] Successful Successful - -
1.9.E11 ${\displaystyle{\displaystyle\overline{z}=x-iy}}$ conjugate(z)= x - I*y Conjugate[z]= x - I*y Failure Failure
Fail
.414213562-.414213562*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}
.414213562+.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}
.414213562+1.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}
-.585786438-.414213562*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}
-.585786438+.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}
-.585786438+1.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}
-1.585786438-.414213562*I <- {z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}
-1.585786438+.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}
-1.585786438+1.585786438*I <- {z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}
.414213562+2.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}
.414213562+3.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}
.414213562+4.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}
-.585786438+2.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}
-.585786438+3.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}
-.585786438+4.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}
-1.585786438+2.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}
-1.585786438+3.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}
-1.585786438+4.414213562*I <- {z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}
-2.414213562+2.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}
-2.414213562+3.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}
-2.414213562+4.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}
-3.414213562+2.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}
-3.414213562+3.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}
-3.414213562+4.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}
-4.414213562+2.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}
-4.414213562+3.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}
-4.414213562+4.414213562*I <- {z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}
-2.414213562-.414213562*I <- {z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}
-2.414213562+.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}
-2.414213562+1.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}
-3.414213562-.414213562*I <- {z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}
-3.414213562+.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}
-3.414213562+1.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}
-4.414213562-.414213562*I <- {z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}
-4.414213562+.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}
-4.414213562+1.585786438*I <- {z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}
Fail
Complex[0.41421356237309515, -0.41421356237309515] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.41421356237309515, 0.5857864376269049] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.41421356237309515, 1.5857864376269049] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.5857864376269049, -0.41421356237309515] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.5857864376269049, 0.5857864376269049] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.5857864376269049, 1.5857864376269049] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5857864376269049, -0.41421356237309515] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5857864376269049, 0.5857864376269049] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.5857864376269049, 1.5857864376269049] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.41421356237309515, 2.414213562373095] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.41421356237309515, 3.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.41421356237309515, 4.414213562373095] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.5857864376269049, 2.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.5857864376269049, 3.414213562373095] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.5857864376269049, 4.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5857864376269049, 2.414213562373095] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5857864376269049, 3.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.5857864376269049, 4.414213562373095] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.414213562373095, 2.414213562373095] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.414213562373095, 3.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.414213562373095, 4.414213562373095] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.414213562373095, 2.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.414213562373095, 3.414213562373095] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.414213562373095, 4.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.414213562373095, 2.414213562373095] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.414213562373095, 3.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.414213562373095, 4.414213562373095] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.414213562373095, -0.41421356237309515] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.414213562373095, 0.5857864376269049] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.414213562373095, 1.5857864376269049] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.414213562373095, -0.41421356237309515] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.414213562373095, 0.5857864376269049] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-3.414213562373095, 1.5857864376269049] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.414213562373095, -0.41421356237309515] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.414213562373095, 0.5857864376269049] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.414213562373095, 1.5857864376269049] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9.E12 ${\displaystyle{\displaystyle|\overline{z}|=|z|}}$ abs(conjugate(z))=abs(z) Abs[Conjugate[z]]=Abs[z] Successful Successful - -
1.9.E13 ${\displaystyle{\displaystyle\operatorname{ph}\overline{z}=-\operatorname{ph}z}}$ argument(conjugate(z))= - argument(z) Arg[Conjugate[z]]= - Arg[z] Failure Failure Successful Successful
1.9.E14 ${\displaystyle{\displaystyle z_{1}+z_{2}=x_{1}+x_{2}+\mathrm{i}(y_{1}+y_{2})}}$ z[1]+ z[2]= x[1]+ x[2]+ I*(y[1]+ y[2]) Subscript[z, 1]+ Subscript[z, 2]= Subscript[x, 1]+ Subscript[x, 2]+ I*(Subscript[y, 1]+ Subscript[y, 2]) Failure Failure Skip Skip
1.9.E14 ${\displaystyle{\displaystyle z_{1}-z_{2}=x_{1}-x_{2}+\mathrm{i}(y_{1}-y_{2})}}$ z[1]- z[2]= x[1]- x[2]+ I*(y[1]- y[2]) Subscript[z, 1]- Subscript[z, 2]= Subscript[x, 1]- Subscript[x, 2]+ I*(Subscript[y, 1]- Subscript[y, 2]) Failure Failure Skip Skip
1.9.E16 ${\displaystyle{\displaystyle\frac{z_{1}}{z_{2}}=\frac{z_{1}\overline{z}_{2}}{|% z_{2}|^{2}}}}$ (z[1])/(z[2])=(z[1]*conjugate(z)[2])/((abs(z[2]))^(2)) Divide[Subscript[z, 1],Subscript[z, 2]]=Divide[Subscript[z, 1]*Subscript[Conjugate[z], 2],(Abs[Subscript[z, 2]])^(2)] Failure Failure Error
Fail
Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-2.0 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -2.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
2.0 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.0, -1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.0, 1.0] <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[Conjugate[z], 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9.E16 ${\displaystyle{\displaystyle\frac{z_{1}\overline{z}_{2}}{|z_{2}|^{2}}=\frac{x_% {1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}}}$ (x[1]*x[2]+ y[1]*y[2]+ I*(x[2]*y[1]- x[1]*y[2]))/(x(x[2])^(2)+ y(y[2])^(2)) Divide[Subscript[x, 1]*Subscript[x, 2]+ Subscript[y, 1]*Subscript[y, 2]+ I*(Subscript[x, 2]*Subscript[y, 1]- Subscript[x, 1]*Subscript[y, 2]),x(Subscript[x, 2])^(2)+ y(Subscript[y, 2])^(2)] Failure Failure Skip Skip
1.9.E18 ${\displaystyle{\displaystyle\operatorname{ph}\left(z_{1}z_{2}\right)=% \operatorname{ph}z_{1}+\operatorname{ph}z_{2}}}$ argument(z[1]*z[2])= argument(z[1])+ argument(z[2]) Arg[Subscript[z, 1]*Subscript[z, 2]]= Arg[Subscript[z, 1]]+ Arg[Subscript[z, 2]] Failure Failure
Fail
6.283185308 <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}
6.283185308 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)-I*2^(1/2)}
6.283185307 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}
-6.283185307 <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}
Fail
6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.9.E19 ${\displaystyle{\displaystyle\left|\frac{z_{1}}{z_{2}}\right|=\frac{|z_{1}|}{|z% _{2}|}}}$ abs((z[1])/(z[2]))=(abs(z[1]))/(abs(z[2])) Abs[Divide[Subscript[z, 1],Subscript[z, 2]]]=Divide[Abs[Subscript[z, 1]],Abs[Subscript[z, 2]]] Successful Successful - -
1.9.E20 ${\displaystyle{\displaystyle\operatorname{ph}\frac{z_{1}}{z_{2}}=\operatorname% {ph}z_{1}-\operatorname{ph}z_{2}}}$ argument((z[1])/(z[2]))= argument(z[1])- argument(z[2]) Arg[Divide[Subscript[z, 1],Subscript[z, 2]]]= Arg[Subscript[z, 1]]- Arg[Subscript[z, 2]] Failure Failure
Fail
6.283185308 <- {z[1] = 2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}
6.283185308 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = 2^(1/2)+I*2^(1/2)}
6.283185307 <- {z[1] = -2^(1/2)-I*2^(1/2), z[2] = -2^(1/2)+I*2^(1/2)}
-6.283185307 <- {z[1] = -2^(1/2)+I*2^(1/2), z[2] = -2^(1/2)-I*2^(1/2)}
Fail
6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
-6.283185307179586 <- {Rule[Subscript[z, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[z, 2], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
1.9.E22 ${\displaystyle{\displaystyle\cos n\theta+i\sin n\theta=(\cos\theta+i\sin\theta% )^{n}}}$ cos(n*theta)+ I*sin(n*theta)=(cos(theta)+ I*sin(theta))^(n) Cos[n*\[Theta]]+ I*Sin[n*\[Theta]]=(Cos[\[Theta]]+ I*Sin[\[Theta]])^(n) Successful Failure - Skip
1.9.E23 ${\displaystyle{\displaystyle\left|\left|z_{1}\right|-\left|z_{2}\right|\right|% <=\left|z_{1}+z_{2}\right|}}$ abs(abs(z[1])- abs(z[2]))< = abs(z[1]+ z[2]) Abs[Abs[Subscript[z, 1]]- Abs[Subscript[z, 2]]]< = Abs[Subscript[z, 1]+ Subscript[z, 2]] Failure Failure Successful Successful
1.9.E23 ${\displaystyle{\displaystyle\left|z_{1}+z_{2}\right|<=\left|z_{1}\right|+\left% |z_{2}\right|}}$ abs(z[1]+ z[2])< = abs(z[1])+ abs(z[2]) Abs[Subscript[z, 1]+ Subscript[z, 2]]< = Abs[Subscript[z, 1]]+ Abs[Subscript[z, 2]] Failure Failure Successful Successful
1.9#Ex9 ${\displaystyle{\displaystyle\frac{\partial u}{\partial x}=\frac{\partial v}{% \partial y}}}$ diff(u, x)= diff(v, y) D[u, x]= D[v, y] Successful Successful - -
1.9#Ex10 ${\displaystyle{\displaystyle\frac{\partial u}{\partial y}=-\frac{\partial v}{% \partial x}}}$ diff(u, y)= - diff(v, x) D[u, y]= - D[v, x] Successful Successful - -
1.9.E26 ${\displaystyle{\displaystyle\frac{{\partial}^{2}u}{{\partial x}^{2}}+\frac{{% \partial}^{2}u}{{\partial y}^{2}}=\frac{{\partial}^{2}v}{{\partial x}^{2}}+% \frac{{\partial}^{2}v}{{\partial y}^{2}}}}$ diff(u, [x$(2)])+ diff(u, [y$(2)])= diff(v, [x$(2)])+ diff(v, [y$(2)]) D[u, {x, 2}]+ D[u, {y, 2}]= D[v, {x, 2}]+ D[v, {y, 2}] Successful Successful - -
1.9.E26 ${\displaystyle{\displaystyle\frac{{\partial}^{2}v}{{\partial x}^{2}}+\frac{{% \partial}^{2}v}{{\partial y}^{2}}=0}}$ diff(v, [x$(2)])+ diff(v, [y$(2)])= 0 D[v, {x, 2}]+ D[v, {y, 2}]= 0 Successful Successful - -
1.9.E27 ${\displaystyle{\displaystyle\frac{{\partial}^{2}u}{{\partial r}^{2}}+\frac{1}{% r}\frac{\partial u}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}u}{{% \partial\theta}^{2}}=0}}$ diff(u, [r$(2)])+(1)/(r)*diff(u, r)+(1)/((r)^(2))*diff(u, [theta$(2)])= 0 D[u, {r, 2}]+Divide[1,r]*D[u, r]+Divide[1,(r)^(2)]*D[u, {\[Theta], 2}]= 0 Successful Successful - -
1.9.E33 ${\displaystyle{\displaystyle u(z)=\frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})% \mathrm{d}\phi}}$ u*(z)=(1)/(2*Pi)*int(u*(z + r*exp(I*phi)), phi = 0..2*Pi) u*(z)=Divide[1,2*Pi]*Integrate[u*(z + r*Exp[I*\[Phi]]), {\[Phi], 0, 2*Pi}] Successful Successful - -
1.9.E34 ${\displaystyle{\displaystyle u(re^{i\theta})=\frac{1}{2\pi}\int^{2\pi}_{0}% \frac{(R^{2}-r^{2})h(Re^{i\phi})\mathrm{d}\phi}{R^{2}-2Rr\cos\left(\phi-\theta% \right)+r^{2}}}}$ u*(r*exp(I*theta))=(1)/(2*Pi)*int((((R)^(2)- (r)^(2))* h*(R*exp(I*phi)))/((R)^(2)- 2*R*r*cos(phi - theta)+ (r)^(2)), phi = 0..2*Pi) u*(r*Exp[I*\[Theta]])=Divide[1,2*Pi]*Integrate[Divide[((R)^(2)- (r)^(2))* h*(R*Exp[I*\[Phi]]),(R)^(2)- 2*R*r*Cos[\[Phi]- \[Theta]]+ (r)^(2)], {\[Phi], 0, 2*Pi}] Error Failure - Skip
1.9.E63 ${\displaystyle{\displaystyle f^{(m)}(z)=\sum_{n=0}^{\infty}{\left(n+1\right)_{% m}}a_{n+m}(z-z_{0})^{n}}}$ (f)^(m)*(z)= sum(pochhammer(n + 1, m)*a[n + m]*(z - z[0])^(n), n = 0..infinity) (f)^(m)*(z)= Sum[Pochhammer[n + 1, m]*Subscript[a, n + m]*(z - Subscript[z, 0])^(n), {n, 0, Infinity}] Failure Failure Skip Successful
1.9.E71 ${\displaystyle{\displaystyle\int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\mathrm{d}t% =\sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\mathrm{d}t}}$ int(sum(f[n]*(t), n = 0..infinity), t = a..b)= sum(int(f[n]*(t), t = a..b), n = 0..infinity) Integrate[Sum[Subscript[f, n]*(t), {n, 0, Infinity}], {t, a, b}]= Sum[Integrate[Subscript[f, n]*(t), {t, a, b}], {n, 0, Infinity}] Successful Failure - Error
1.10.E20 ${\displaystyle{\displaystyle|\ln\left(1+a_{n}(z)\right)|<=M_{n}}}$ abs(ln(1 + a[n]*(z)))< = M[n] Abs[Log[1 + Subscript[a, n]*(z)]]< = Subscript[M, n] Failure Failure Skip Successful
1.12.E26 ${\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta<\operatorname{ph}b_{n}}}$ -(1)/(2)*Pi + delta < argument(b[n]) -Divide[1,2]*Pi + \[Delta]< Arg[Subscript[b, n]] Failure Failure Successful Successful
1.12.E26 ${\displaystyle{\displaystyle\operatorname{ph}b_{n}<\tfrac{1}{2}\pi-\delta}}$ argument(b[n])<(1)/(2)*Pi - delta Arg[Subscript[b, n]]<Divide[1,2]*Pi - \[Delta] Failure Failure Successful Successful
1.12.E27 ${\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta<\operatorname{ph}C_{n}}}$ -(1)/(2)*Pi + delta < argument(C[n]) -Divide[1,2]*Pi + \[Delta]< Arg[Subscript[C, n]] Failure Failure Successful Successful
1.12.E27 ${\displaystyle{\displaystyle\operatorname{ph}C_{n}<\tfrac{1}{2}\pi-\delta}}$ argument(C[n])<(1)/(2)*Pi - delta Arg[Subscript[C, n]]<Divide[1,2]*Pi - \[Delta] Failure Failure Successful Successful
1.13.E11 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}\xi}^{2}}+F(% \xi)\frac{\mathrm{d}W}{\mathrm{d}\xi}+G(\xi)W=0}}$ diff(W, [xi$(2)])+ F*(xi)* diff(W, xi)+ G*(xi)* W = 0 D[W, {\[Xi], 2}]+ F*(\[Xi])* D[W, \[Xi]]+ G*(\[Xi])* W = 0 Failure Failure Fail -5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} 5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} 5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} -5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} 5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} 5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} -5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} -5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} 5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} -5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} -5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} 5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} -5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} -5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} 5.656854245+5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} 5.656854245-5.656854245*I <- {G = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} 5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} 5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} -5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} -5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} 5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} -5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} -5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} 5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} -5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} -5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} 5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} 5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} -5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} 5.656854245+5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} 5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} -5.656854245-5.656854245*I <- {G = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} 5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} -5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} -5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} 5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} -5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} -5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} 5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} 5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} -5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} 5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} 5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} -5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} 5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} 5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} -5.656854245-5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} -5.656854245+5.656854245*I <- {G = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} -5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} -5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} 5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} 5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} -5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} 5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} 5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} -5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} 5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} 5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} -5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} -5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} 5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)+I*2^(1/2)} -5.656854245-5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = 2^(1/2)-I*2^(1/2)} -5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)-I*2^(1/2)} 5.656854245+5.656854245*I <- {G = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), xi = -2^(1/2)+I*2^(1/2)} Fail Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, -5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[5.656854249492381, 5.656854249492381] <- {Rule[G, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[ξ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} 1.13.E14 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}z}^{2}}-H(z)W=% 0}}$ diff(W, [z$(2)])- H*(z)* W = 0 D[W, {z, 2}]- H*(z)* W = 0 Failure Failure
Fail
5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = 2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
5.656854245+5.656854245*I <- {H = 2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
5.656854245+5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
5.656854245-5.656854245*I <- {H = -2^(1/2)-I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
5.656854245+5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-5.656854245-5.656854245*I <- {H = -2^(1/2)+I*2^(1/2), W = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
Fail
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -5.656854249492381] <- {Rule[H, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[W, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.13#Ex8 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}U}{{\mathrm{d}z}^{2}}+IU=0}}$ diff(U, [z$(2)])+ I*U = 0 D[U, {z, 2}]+ I*U = 0 Failure Failure Fail -1.414213562+1.414213562*I <- {U = 2^(1/2)+I*2^(1/2)} 1.414213562+1.414213562*I <- {U = 2^(1/2)-I*2^(1/2)} 1.414213562-1.414213562*I <- {U = -2^(1/2)-I*2^(1/2)} -1.414213562-1.414213562*I <- {U = -2^(1/2)+I*2^(1/2)} Fail Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[U, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[U, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[U, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[U, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} 1.13#Ex9 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}V}{{\mathrm{d}z}^{2}}+JV=0}}$ diff(V, [z$(2)])+ J*V = 0 D[V, {z, 2}]+ J*V = 0 Failure Failure
Fail
0.+3.999999998*I <- {J = 2^(1/2)+I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}
3.999999998+0.*I <- {J = 2^(1/2)+I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}
0.-3.999999998*I <- {J = 2^(1/2)+I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}
-3.999999998+0.*I <- {J = 2^(1/2)+I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}
3.999999998+0.*I <- {J = 2^(1/2)-I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}
0.-3.999999998*I <- {J = 2^(1/2)-I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}
-3.999999998+0.*I <- {J = 2^(1/2)-I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}
0.+3.999999998*I <- {J = 2^(1/2)-I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}
0.-3.999999998*I <- {J = -2^(1/2)-I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}
-3.999999998+0.*I <- {J = -2^(1/2)-I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}
0.+3.999999998*I <- {J = -2^(1/2)-I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}
3.999999998+0.*I <- {J = -2^(1/2)-I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}
-3.999999998+0.*I <- {J = -2^(1/2)+I*2^(1/2), V = 2^(1/2)+I*2^(1/2)}
0.+3.999999998*I <- {J = -2^(1/2)+I*2^(1/2), V = 2^(1/2)-I*2^(1/2)}
3.999999998+0.*I <- {J = -2^(1/2)+I*2^(1/2), V = -2^(1/2)-I*2^(1/2)}
0.-3.999999998*I <- {J = -2^(1/2)+I*2^(1/2), V = -2^(1/2)+I*2^(1/2)}
Fail
Complex[0.0, 4.0] <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
4.0 <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -4.0] <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-4.0 <- {Rule[J, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
4.0 <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -4.0] <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-4.0 <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 4.0] <- {Rule[J, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -4.0] <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-4.0 <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 4.0] <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
4.0 <- {Rule[J, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
-4.0 <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 4.0] <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
4.0 <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -4.0] <- {Rule[J, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[V, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.14.E6 ${\displaystyle{\displaystyle(f*g)(t)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-% \infty}F(x)G(x)e^{-itx}\mathrm{d}x}}$ (f * g)*(t)=(1)/(sqrt(2*Pi))*int(F*(x)* G*(x)* exp(- I*t*x), x = - infinity..infinity) (f * g)*(t)=Divide[1,Sqrt[2*Pi]]*Integrate[F*(x)* G*(x)* Exp[- I*t*x], {x, - Infinity, Infinity}] Failure Failure Skip Skip
1.15.E13 ${\displaystyle{\displaystyle\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\mathrm{d}% \theta=1}}$ (1)/(2*Pi)*int(P*(r , theta), theta = 0..2*Pi)= 1 Divide[1,2*Pi]*Integrate[P*(r , \[Theta]), {\[Theta], 0, 2*Pi}]= 1 Error Failure - Error
1.15.E16 ${\displaystyle{\displaystyle\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\mathrm{% d}\theta=1}}$ (1)/(2*Pi)*int(K[n]*(theta), theta = 0..2*Pi)= 1 Divide[1,2*Pi]*Integrate[Subscript[K, n]*(\[Theta]), {\[Theta], 0, 2*Pi}]= 1 Failure Failure Skip
Fail
Complex[3.442882938158366, 4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.442882938158366, -4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.442882938158366, -4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.442882938158366, 4.442882938158366] <- {Rule[Subscript[K, n], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.15.E34 ${\displaystyle{\displaystyle\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\mathrm% {d}x=1}}$ (1)/(2*Pi)*int(P*(x , y), x = - infinity..infinity)= 1 Divide[1,2*Pi]*Integrate[P*(x , y), {x, - Infinity, Infinity}]= 1 Error Failure - Error
1.15.E36 ${\displaystyle{\displaystyle h(x,y)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-% \infty}e^{-y|t|}e^{-ixt}F(t)\mathrm{d}t}}$ h*(x , y)=(1)/(sqrt(2*Pi))*int(exp(- y*abs(t))*exp(- I*x*t)*F*(t), t = - infinity..infinity) h*(x , y)=Divide[1,Sqrt[2*Pi]]*Integrate[Exp[- y*Abs[t]]*Exp[- I*x*t]*F*(t), {t, - Infinity, Infinity}] Failure Failure Skip Error
1.15.E39 ${\displaystyle{\displaystyle\Phi(z)=\Phi(x+iy)}}$ Phi*(z)= Phi*(x + I*y) \[CapitalPhi]*(z)= \[CapitalPhi]*(x + I*y) Failure Failure
Fail
0.+1.171572874*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}
1.414213562-.242640688*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}
2.828427124-1.656854250*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}
-1.414213562-.242640688*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}
0.-1.656854250*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}
1.414213562-3.071067812*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}
-2.828427124-1.656854250*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}
-1.414213562-3.071067812*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}
0.-4.485281374*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}
3.999999998-2.828427124*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}
5.414213560-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}
6.828427122-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}
2.585786436-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}
3.999999998-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}
5.414213560-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}
1.171572874-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}
2.585786436-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}
3.999999998-8.485281372*I <- {Phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}
0.-6.828427122*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}
1.414213562-8.242640684*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}
2.828427124-9.656854246*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}
-1.414213562-8.242640684*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}
0.-9.656854246*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}
1.414213562-11.07106781*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}
-2.828427124-9.656854246*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}
-1.414213562-11.07106781*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}
0.-12.48528137*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}
-3.999999998-2.828427124*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}
-2.585786436-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}
-1.171572874-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}
-5.414213560-4.242640686*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}
-3.999999998-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}
-2.585786436-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}
-6.828427122-5.656854248*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}
-5.414213560-7.071067810*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}
-3.999999998-8.485281372*I <- {Phi = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}
1.171572874+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}
-.242640688-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}
-1.656854250-2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}
-.242640688+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}
-1.656854250+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}
-3.071067812-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}
-1.656854250+2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}
-3.071067812+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}
-4.485281374+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}
-2.828427124-3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}
-4.242640686-5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}
-5.656854248-6.828427122*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}
-4.242640686-2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}
-5.656854248-3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}
-7.071067810-5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}
-5.656854248-1.171572874*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}
-7.071067810-2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}
-8.485281372-3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}
-6.828427122+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}
-8.242640684-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}
-9.656854246-2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}
-8.242640684+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}
-9.656854246+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}
-11.07106781-1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}
-9.656854246+2.828427124*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}
-11.07106781+1.414213562*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}
-12.48528137+0.*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}
-2.828427124+3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}
-4.242640686+2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}
-5.656854248+1.171572874*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}
-4.242640686+5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}
-5.656854248+3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}
-7.071067810+2.585786436*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}
-5.656854248+6.828427122*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}
-7.071067810+5.414213560*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}
-8.485281372+3.999999998*I <- {Phi = 2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}
0.-1.171572874*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}
-1.414213562+.242640688*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}
-2.828427124+1.656854250*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}
1.414213562+.242640688*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}
0.+1.656854250*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}
-1.414213562+3.071067812*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}
2.828427124+1.656854250*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}
1.414213562+3.071067812*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}
0.+4.485281374*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}
-3.999999998+2.828427124*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}
-5.414213560+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}
-6.828427122+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}
-2.585786436+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}
-3.999999998+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}
-5.414213560+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}
-1.171572874+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}
-2.585786436+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}
-3.999999998+8.485281372*I <- {Phi = -2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}
0.+6.828427122*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}
-1.414213562+8.242640684*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}
-2.828427124+9.656854246*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}
1.414213562+8.242640684*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}
0.+9.656854246*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}
-1.414213562+11.07106781*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}
2.828427124+9.656854246*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}
1.414213562+11.07106781*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}
0.+12.48528137*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}
3.999999998+2.828427124*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}
2.585786436+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}
1.171572874+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}
5.414213560+4.242640686*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}
3.999999998+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}
2.585786436+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}
6.828427122+5.656854248*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}
5.414213560+7.071067810*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}
3.999999998+8.485281372*I <- {Phi = -2^(1/2)-I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}
-1.171572874+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 1}
.242640688+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 2}
1.656854250+2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 1, y = 3}
.242640688-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 1}
1.656854250+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 2}
3.071067812+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 2, y = 3}
1.656854250-2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 1}
3.071067812-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 2}
4.485281374+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), x = 3, y = 3}
2.828427124+3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 1}
4.242640686+5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 2}
5.656854248+6.828427122*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 1, y = 3}
4.242640686+2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 1}
5.656854248+3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 2}
7.071067810+5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 2, y = 3}
5.656854248+1.171572874*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 1}
7.071067810+2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 2}
8.485281372+3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), x = 3, y = 3}
6.828427122+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 1}
8.242640684+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 2}
9.656854246+2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 1, y = 3}
8.242640684-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 1}
9.656854246+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 2}
11.07106781+1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 2, y = 3}
9.656854246-2.828427124*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 1}
11.07106781-1.414213562*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 2}
12.48528137+0.*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2), x = 3, y = 3}
2.828427124-3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 1}
4.242640686-2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 2}
5.656854248-1.171572874*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 1, y = 3}
4.242640686-5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 1}
5.656854248-3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 2}
7.071067810-2.585786436*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 2, y = 3}
5.656854248-6.828427122*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 1}
7.071067810-5.414213560*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 2}
8.485281372-3.999999998*I <- {Phi = -2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2), x = 3, y = 3}
Fail
Complex[0.0, 1.1715728752538097] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.4142135623730951, -0.24264068711928566] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[2.8284271247461903, -1.6568542494923806] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4142135623730951, -0.24264068711928566] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -1.6568542494923806] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.4142135623730951, -3.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, -1.6568542494923806] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4142135623730951, -3.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -4.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
1.1715728752538097 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.24264068711928566, -1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6568542494923806, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.24264068711928566, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-1.6568542494923806 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.0710678118654755, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6568542494923806, 2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-3.0710678118654755, 1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-4.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -1.1715728752538097] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4142135623730951, 0.24264068711928566] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, 1.6568542494923806] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.4142135623730951, 0.24264068711928566] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 1.6568542494923806] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4142135623730951, 3.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[2.8284271247461903, 1.6568542494923806] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.4142135623730951, 3.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 4.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
-1.1715728752538097 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.24264068711928566, 1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.6568542494923806, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.24264068711928566, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.6568542494923806 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.0710678118654755, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.6568542494923806, -2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[3.0710678118654755, -1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
4.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.0, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.414213562373095, -4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[6.82842712474619, -5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[2.585786437626905, -4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.0, -5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.414213562373095, -7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.1715728752538097, -5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[2.585786437626905, -7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.0, -8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, -4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.242640687119286, -5.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -6.82842712474619] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.242640687119286, -2.585786437626905] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.0710678118654755, -5.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, -1.1715728752538097] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.0710678118654755, -2.585786437626905] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-8.485281374238571, -4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.0, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.414213562373095, 4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-6.82842712474619, 5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.585786437626905, 4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.0, 5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.414213562373095, 7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.1715728752538097, 5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.585786437626905, 7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.0, 8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[2.8284271247461903, 4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.242640687119286, 5.414213562373095] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 6.82842712474619] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.242640687119286, 2.585786437626905] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.0710678118654755, 5.414213562373095] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, 1.1715728752538097] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.0710678118654755, 2.585786437626905] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.485281374238571, 4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -6.82842712474619] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.4142135623730951, -8.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[2.8284271247461903, -9.65685424949238] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4142135623730951, -8.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -9.65685424949238] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.4142135623730951, -11.071067811865476] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, -9.65685424949238] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.4142135623730951, -11.071067811865476] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.0, -12.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
-6.82842712474619 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-8.242640687119286, -1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-9.65685424949238, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-8.242640687119286, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-9.65685424949238 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-11.071067811865476, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-9.65685424949238, 2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-11.071067811865476, 1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
-12.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 6.82842712474619] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4142135623730951, 8.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, 9.65685424949238] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.4142135623730951, 8.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 9.65685424949238] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.4142135623730951, 11.071067811865476] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[2.8284271247461903, 9.65685424949238] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.4142135623730951, 11.071067811865476] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[0.0, 12.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
6.82842712474619 <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.242640687119286, 1.4142135623730951] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.65685424949238, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.242640687119286, -1.4142135623730951] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.65685424949238 <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.071067811865476, 1.4142135623730951] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.65685424949238, -2.8284271247461903] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.071067811865476, -1.4142135623730951] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
12.485281374238571 <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.0, -2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.585786437626905, -4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.1715728752538097, -5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.414213562373095, -4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.0, -5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.585786437626905, -7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-6.82842712474619, -5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5.414213562373095, -7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-4.0, -8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, 4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.242640687119286, 2.585786437626905] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 1.1715728752538097] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-4.242640687119286, 5.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.0710678118654755, 2.585786437626905] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-5.656854249492381, 6.82842712474619] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-7.0710678118654755, 5.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-8.485281374238571, 4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.0, 2.8284271247461903] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[2.585786437626905, 4.242640687119286] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.1715728752538097, 5.656854249492381] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.414213562373095, 4.242640687119286] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.0, 5.656854249492381] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[2.585786437626905, 7.0710678118654755] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[6.82842712474619, 5.656854249492381] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[5.414213562373095, 7.0710678118654755] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[4.0, 8.485281374238571] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[2.8284271247461903, -4.0] <- {Rule[x, 1], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.242640687119286, -2.585786437626905] <- {Rule[x, 1], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -1.1715728752538097] <- {Rule[x, 1], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.242640687119286, -5.414213562373095] <- {Rule[x, 2], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -4.0] <- {Rule[x, 2], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.0710678118654755, -2.585786437626905] <- {Rule[x, 2], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[5.656854249492381, -6.82842712474619] <- {Rule[x, 3], Rule[y, 1], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[7.0710678118654755, -5.414213562373095] <- {Rule[x, 3], Rule[y, 2], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[8.485281374238571, -4.0] <- {Rule[x, 3], Rule[y, 3], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Φ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.15.E42 ${\displaystyle{\displaystyle\int^{\infty}_{-\infty}K_{R}(s)\mathrm{d}s=1}}$ int(K[R]*(s), s = - infinity..infinity)= 1 Integrate[Subscript[K, R]*(s), {s, - Infinity, Infinity}]= 1 Failure Failure Skip
Fail
Complex[0.41421356237309515, 1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.41421356237309515, -1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.414213562373095, -1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.414213562373095, 1.4142135623730951] <- {Rule[Integrate[Times[s, Subscript[K, R]], {s, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.15.E44 ${\displaystyle{\displaystyle\sigma_{R}(\theta)=\frac{1}{\sqrt{2\pi}}\int^{R}_{% -R}\left(1-\frac{|t|}{R}\right)e^{-i\theta t}F(t)\mathrm{d}t}}$ sigma[R]*(theta)=(1)/(sqrt(2*Pi))*int((1 -(abs(t))/(R))* exp(- I*theta*t)*F*(t), t = - R..R) Subscript[\[Sigma], R]*(\[Theta])=Divide[1,Sqrt[2*Pi]]*Integrate[(1 -Divide[Abs[t],R])* Exp[- I*\[Theta]*t]*F*(t), {t, - R, R}] Failure Failure Skip Successful
1.16.E19 ${\displaystyle{\displaystyle x^{\alpha}_{+}=x^{\alpha}H\left(x\right)}}$ (x[+])^(alpha)= (x)^(alpha)* Heaviside(x) (Subscript[x, +])^(\[Alpha])= (x)^(\[Alpha])* HeavisideTheta[x] Error Failure - Error
1.16#Ex1 ${\displaystyle{\displaystyle F(\mathbf{x})=F}}$ F*(x)= F F*(x)= F Failure Failure
Fail
1.414213562+1.414213562*I <- {F = 2^(1/2)+I*2^(1/2), x = 2}
2.828427124+2.828427124*I <- {F = 2^(1/2)+I*2^(1/2), x = 3}
1.414213562-1.414213562*I <- {F = 2^(1/2)-I*2^(1/2), x = 2}
2.828427124-2.828427124*I <- {F = 2^(1/2)-I*2^(1/2), x = 3}
-1.414213562-1.414213562*I <- {F = -2^(1/2)-I*2^(1/2), x = 2}
-2.828427124-2.828427124*I <- {F = -2^(1/2)-I*2^(1/2), x = 3}
-1.414213562+1.414213562*I <- {F = -2^(1/2)+I*2^(1/2), x = 2}
-2.828427124+2.828427124*I <- {F = -2^(1/2)+I*2^(1/2), x = 3}
Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}
Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[F, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}
Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[F, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}
Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[F, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}
Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[F, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 2]}
Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[F, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[x, 3]}
Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[F, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2]}
Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[F, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3]}
1.16#Ex2 ${\displaystyle{\displaystyle D_{\boldsymbol{{\alpha}}}={\mathrm{i}^{-|% \boldsymbol{{\alpha}}|}}D^{\boldsymbol{{\alpha}}}}}$ D[alpha]= (I)^(-abs(alpha))* (D)^(alpha) Subscript[D, \[Alpha]]= (I)^(-Abs[\[Alpha]])* (D)^(\[Alpha]) Failure Failure
Fail
.9779681321+2.175809568*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
.9779681321-.6526175556*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.850458992-.6526175556*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.850458992+2.175809568*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
9.438272386+2.467033025*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
9.438272386-.361394099*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
6.609845262-.361394099*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
6.609845262+2.467033025*I <- {D = 2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
.8479100469+.4255625275*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
.8479100469-2.402864596*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.980517077-2.402864596*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.980517077+.4255625275*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
1.536729595+1.398138497*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
1.536729595-1.430288627*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.291697529-1.430288627*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.291697529+1.398138497*I <- {D = 2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
9.438272386+.361394099*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
9.438272386-2.467033025*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
6.609845262-2.467033025*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
6.609845262+.361394099*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
.9779681321+.6526175556*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
.9779681321-2.175809568*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.850458992-2.175809568*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.850458992+.6526175556*I <- {D = 2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
1.536729595+1.430288627*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
1.536729595-1.398138497*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.291697529-1.398138497*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.291697529+1.430288627*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
.8479100469+2.402864596*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
.8479100469-.4255625275*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.980517077-.4255625275*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.980517077+2.402864596*I <- {D = 2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
-51.12384670-51.57661382*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
-51.12384670-54.40504094*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-53.95227382-54.40504094*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-53.95227382-51.57661382*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
1.377148458+1.501888445*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
1.377148458-1.326538679*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.451278666-1.326538679*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.451278666+1.501888445*I <- {D = -2^(1/2)-I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
1.404778314+1.423730122*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
1.404778314-1.404697002*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.423648810-1.404697002*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.423648810+1.423730122*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
-2.676538322-8.262170665*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
-2.676538322-11.09059779*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-5.504965446-11.09059779*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-5.504965446-8.262170665*I <- {D = -2^(1/2)-I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
1.377148458+1.326538679*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
1.377148458-1.501888445*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.451278666-1.501888445*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.451278666+1.326538679*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
-51.12384670+54.40504094*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
-51.12384670+51.57661382*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-53.95227382+51.57661382*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-53.95227382+54.40504094*I <- {D = -2^(1/2)+I*2^(1/2), alpha = 2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
-2.676538322+11.09059779*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
-2.676538322+8.262170665*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-5.504965446+8.262170665*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-5.504965446+11.09059779*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)-I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
1.404778314+1.404697002*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)+I*2^(1/2)}
1.404778314-1.423730122*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = 2^(1/2)-I*2^(1/2)}
-1.423648810-1.423730122*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)-I*2^(1/2)}
-1.423648810+1.404697002*I <- {D = -2^(1/2)+I*2^(1/2), alpha = -2^(1/2)+I*2^(1/2), D[alpha] = -2^(1/2)+I*2^(1/2)}
Successful
1.16.E32 ${\displaystyle{\displaystyle P(\mathbf{D})=\sum_{\boldsymbol{{\alpha}}}c_{% \boldsymbol{{\alpha}}}\mathbf{D}^{\alpha}}}$ P*(D)= sum(c[alpha]*(D)^(alpha), alpha = - infinity..infinity) P*(D)= Sum[Subscript[c, \[Alpha]]*(D)^(\[Alpha]), {\[Alpha], - Infinity, Infinity}] Failure Failure Skip Skip
1.16.E40 ${\displaystyle{\displaystyle\int^{\infty}_{-\infty}\delta\left(t\right){% \mathrm{e}^{\mathrm{i}xt}}\mathrm{d}t=1}}$ int(Dirac(t)*exp(I*x*t), t = - infinity..infinity)= 1 Integrate[DiracDelta[t]*Exp[I*x*t], {t, - Infinity, Infinity}]= 1 Successful Successful - -
1.16.E43 ${\displaystyle{\displaystyle\frac{1}{2\pi}\int^{\infty}_{-\infty}{\mathrm{e}^{% \mathrm{i}xt}}\mathrm{d}t=\delta\left(x\right)}}$ (1)/(2*Pi)*int(exp(I*x*t), t = - infinity..infinity)= Dirac(x) Divide[1,2*Pi]*Integrate[Exp[I*x*t], {t, - Infinity, Infinity}]= DiracDelta[x] Successful Failure -
Fail
Complex[-1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.6392926414123716, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.6392926414123716, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.1891344833338187, 1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.1891344833338187, 1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.6392926414123716, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.6392926414123716, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.1891344833338187, -1.6392926414123716] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[1.1891344833338187, -1.1891344833338187] <- {Rule[DiracDelta[x], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]], Rule[Integrate[Power[E, Times[Complex[0, 1], t, x]], {t, DirectedInfinity[-1], DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
1.16.E44 ${\displaystyle{\displaystyle\operatorname{sign}\left(x\right)=2H\left(x\right)% -1}}$ signum(x)= 2*Heaviside(x)- 1 Sign[x]= 2*HeavisideTheta[x]- 1 Failure Failure Skip Successful
1.17.E1 ${\displaystyle{\displaystyle\delta\left(x\right)=0}}$ Dirac(x)= 0 DiracDelta[x]= 0 Error Failure - Successful
1.17.E2 ${\displaystyle{\displaystyle\int_{-\infty}^{\infty}\delta\left(x-a\right)\phi(% x)\mathrm{d}x=\phi(a)}}$ int(Dirac(x - a)*phi*(x), x = - infinity..infinity)= phi*(a) Integrate[DiracDelta[x - a]*\[Phi]*(x), {x, - Infinity, Infinity}]= \[Phi]*(a) Successful Failure - Successful
1.17.E6 ${\displaystyle{\displaystyle\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty% }^{\infty}e^{-n(x-a)^{2}}\phi(x)\mathrm{d}x=\phi(a)}}$ limit(sqrt((n)/(Pi))*int(exp(- n*(x - a)^(2))*phi*(x), x = - infinity..infinity), n = infinity)= phi*(a) Limit[Sqrt[Divide[n,Pi]]*Integrate[Exp[- n*(x - a)^(2)]*\[Phi]*(x), {x, - Infinity, Infinity}], n -> Infinity]= \[Phi]*(a) Successful Failure - Error
1.17.E7