# Definition:Circle Group

## Contents

## 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

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 12$: Example $12.1$ - 1971: Allan Clark:
*Elements of Abstract Algebra*... (previous) ... (next): Chapter $2$: Examples of Group Structure: $\S 31$