DLMF:4.4.E11 (Q1545)

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DLMF:4.4.E11
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    Statements

    Defining formula
    e ± 3 ⁢ π ⁢ i / 4 = - 1 2 ± i ⁢ 1 2 , superscript 𝑒 plus-or-minus 3 𝜋 imaginary-unit 4 plus-or-minus 1 2 imaginary-unit 1 2 {\displaystyle{\displaystyle e^{\pm 3\pi\mathrm{i}/4}=-\frac{1}{\sqrt{2}}\pm% \mathrm{i}\frac{1}{\sqrt{2}},}}
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    DLMF id
    DLMF:4.4.E11
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2agdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
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