Definition:Circle Group

Definition
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.

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

Also see

 * Circle Group is Group