Definition:Circle Group

Definition
Let $K$ be the set of all complex numbers of unit modulus:


 * $K = \left\{{z \in \C: \left|{z}\right| = 1}\right\}$

Consider the algebraic structure $\left({K, \times}\right)$ where $\times$ denotes the operation of complex multiplication.

Then $\left({K, \times}\right)$ is called the circle group.

Also known as
It is also seen with the fuller title the complex unit circle (group).

Also see

 * Circle Group is a Group