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Mathematics-Online course: Preparatory Course Mathematics - Basics - Complex Numbers

Complex Conjugation

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For every complex number $ z=x+\mathrm{i}y$ its complex conjugate is defined as

$\displaystyle \bar z = x - \mathrm{i}y \,. $

Geometrically, complex conjugation is a reflection along the $ x$-axis: $ (x,y)\to(x,-y)$.

Complex conjugation is compatible with arithmetic operations:

$\displaystyle \overline{z_1\circ z_2} = \bar z_1 \circ \bar z_2 $

for $ \circ = +,-,*,/$.

(Authors: Höllig/Abele)
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  automatically generated 1/9/2017