Definition:Root of Unity/Complex/Order

Definition

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

Let $U_n$ denote the complex $n$th roots of unity:

$U_n = \set {z \in \C: z^n = 1}$

Let $z \in U_n$.

The order of $z$ is the smallest $p \in \Z_{> 0}$ such that:

$z^p = 1$