Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online lexicon:

Multiplication of Complex Numbers

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 overview

The product $ z_1z_2$ of two complex numbers

$\displaystyle z_k = x_k + \mathrm{i} y_k =
r_k \exp(\mathrm{i}\varphi_k)


$\displaystyle (x_1x_2-y_1y_2) + (x_1y_2+x_2y_1)\mathrm{i} =
r_1r_2 \exp(\mathrm{i}(\varphi_1+\varphi_2))\,


Geometrically speaking, multiplication with a complex number $ z=r e^{\mathrm{i}\varphi}$ corresponds to a dilation with scale factor $ r$ and a rotation by $ \varphi$.

(Authors: Höllig/Kopf/Abele)

[Examples] [Links]

  automatically generated 6/11/2007