\begin{definition}[Definition:Group of Gaussian Integer Units]
Let $i$ be the imaginary unit: $i = \sqrt {-1}$.
Let $U_\C$ be the set of complex numbers defined as:
:$U_\C = \set {1, i, -1, -i}$
Let $\times$ denote the operation of complex multiplication.
The algebraic structure $\struct {U_\C, \times}$ is the '''group of units of the ring of Gaussian integers'''.
\end{definition}