Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online course: Basic Mathematics - Complex Numbers

Complex Roots of Unity

[previous page] [next page] [table of contents][page overview]

The equation

$\displaystyle z^n = 1 $

has exactly $ n$ 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 $ n$ -th roots of unity form a regular $ n$ -polygon inscribed in the unit circle.

(Authors: Höllig/Kopf/Abele)

(temporary unavailable)
[previous page] [next page] [table of contents][page overview]
  automatically generated 10/31/2008