\begin{definition}[Definition:Root of Unity/Complex/Primitive]
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''' {{iff}} its order is $n$.
\end{definition}