\begin{definition}[Definition:Root of Unity/Complex/Order]
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:
:$z^p = 1$
Category:Definitions/Complex Roots of Unity
\end{definition}