\begin{definition}[Definition:Circle Group]
Let $K$ be the set of all complex numbers of unit modulus:
:$K = \set {z \in \C: \cmod z = 1}$
Consider the algebraic structure $\struct {K, \times}$ where $\times$ denotes the operation of complex multiplication.
Then $\struct {K, \times}$ is called the '''circle group'''.
\end{definition}