Unit Complex Number

Unit Complex Number

## Definition / Concept

A complex number having modulus $1$ lies on the unit circle.

## Formula

$$|z|=1$$

Therefore:

$$z=\cos\theta+i\sin\theta$$

or:

$$z=e^{i\theta}$$

## Conditions / Special Cases

For every unit complex number:

$$z\bar z=1$$

Therefore:

$$\bar z=\frac1z$$

## Usage

- Used in roots of unity, polar form and rotational problems.