◀ ▲ ▶Branches / Analysis / Proposition: n-th Roots of Unity
Proposition: n-th Roots of Unity
Let $n\in\mathbb Z$ be an integer. The equality $z^n=1$ has exactly $n$ complex solutions, i.e. $$\zeta_k=\exp\left(2\pi i\frac{k}{n}\right),\quad\quad k=0,1,\ldots,n-1,$$
called the $n$-th roots of unity. In particular, $\zeta_k=\zeta_m$ for any two integers $k,m$ being congruent $k(n)\equiv m(n)$ modulo $n.$
Table of Contents
Proofs: 1
Mentioned in:
Chapters: 1
Lemmas: 2
Thank you to the contributors under CC BY-SA 4.0! 
- Github:
-
References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
