\begin{definition}[Definition:Root of Unity/Complex/First]
Let $n \in \Z_{>0}$ be a (strictly) positive integer.
In Complex Roots of Unity in Exponential Form it is shown that the complex $n$th roots of unity are the elements of the set:
:$U_n = \set {e^{2 i k \pi / n}: k \in \N_n}$
The root $e^{2 i \pi / n}$ is known as the '''first (complex) $n$th root of unity'''.
\end{definition}