Definition:Root of Unity/Complex/Primitive

Definition
Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $U_n$ denote the complex $n$th roots of unity:
 * $U_n = \set {z \in \C: z^n = 1}$

A primitive (complex) $n$th root of unity is an element $\alpha \in U_n$ such that:


 * $U_n = \set {1, \alpha, \alpha^2, \ldots, \alpha^{n - 1} }$

Equivalently, an $n$th root of unity is primitive its order is $n$.