# Definition:Circle Group

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## 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).