Mathematics-Online lexicon: Complex Conjugation

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	Mathematics-Online lexicon:
	Complex Conjugation

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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

-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)

automatically generated 6/11/2007