DLMF:1.9.E16 (Q290): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2afdec

Revision as of 16:06, 1 January 2020

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DLMF:1.9.E16
No description defined

    Statements

    Defining formula
    z 1 z 2 = z 1 ⁢ z ¯ 2 | z 2 | 2 = x 1 ⁢ x 2 + y 1 ⁢ y 2 + i ⁢ ( x 2 ⁢ y 1 - x 1 ⁢ y 2 ) x 2 2 + y 2 2 , subscript 𝑧 1 subscript 𝑧 2 subscript 𝑧 1 subscript 𝑧 2 superscript subscript 𝑧 2 2 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 superscript subscript 𝑥 2 2 superscript subscript 𝑦 2 2 {\displaystyle{\displaystyle\frac{z_{1}}{z_{2}}=\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}},}}
    0 references
    DLMF id
    DLMF:1.9.E16
    0 references
    Symbols used
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
    0 references
     
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