Definition:Group of Gaussian Integer Units

Definition
Let $i$ be the imaginary unit: $i = \sqrt {-1}$.

Let $U_\C$ be the set of complex numbers defined as:
 * $U_\C = \left\{{1, i, -1, -i}\right\}$

Let $\times$ denote the operation of complex multiplication.

The algebraic structure $\left({U_\C, \times}\right)$ is the group of units of the ring of Gaussian integers.

Cayley Table
The Cayley table for $\left({U_\C, \times}\right)$ is as follows:

Also see

 * Units of Gaussian Integers, where it is shown that $U_\C$ is the set of units of the ring of Gaussian integers'''


 * Units of Gaussian Integers form Group