\begin{definition}[Definition:Multiplicative Group of Complex Roots of Unity]
Let $n \in \Z$ be an integer such that $n > 0$.
Let $U_n := \set {z \in \C: z^n = 1}$ denote the set of complex $n$th roots of unity.
Let $\struct {U_n, \times}$ be the algebraic structure formed by $U_n$ under complex multiplication.
Then $\struct {U_n, \times}$ is the '''multiplicative group of complex $n$th roots of unity'''.
\end{definition}