Mathematics-Online lexicon: Complex Roots of Unity

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	Mathematics-Online lexicon:
	Complex Roots of Unity

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

The equation

$\displaystyle z^n = 1$

has exactly

solutions in $\mathbb{C}$

$\displaystyle z_k = w_n^k,\quad w_n = \exp(2\pi\mathrm{i}/n), \quad k=0,\ldots,n-1\,.$

Those are called complex roots of unity

$\includegraphics[width=0.5\linewidth]{Bild_Einheitswurzel.eps}$

As illustrated in the figure the -th roots of unity form a regular -polygon inscribed in the unit circle.

(Authors: Höllig/Kopf/Abele)

Example:

automatically generated 10/ 4/2007