Definition:Circle Group

Definition
Let $\mathbb S$ be the set of all complex numbers of unit modulus:


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

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

Then $\left({\mathbb S, \times}\right)$ 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