Units of Gaussian Integers form Group

Theorem
Let $U_\C$ be the set of units of the Gaussian integers:
 * $U_\C = \set {1, i, -1, -i}$

where $i$ is the imaginary unit: $i = \sqrt {-1}$.

Let $\struct {U_\C, \times}$ be the algebraic structure formed by $U_\C$ under the operation of complex multiplication.

Then $\struct {U_\C, \times}$ forms a cyclic group under complex multiplication.