Modulus of a Complex Number

Modulus of a Complex Number

## Definition / Concept

The modulus of a complex number represents its distance from the origin in the complex plane.

## Formula

If:

$$z=a+ib$$

then:

$$|z|=\sqrt{a^2+b^2}$$

Also:

$$|z|^2=z\bar z$$

## Conditions / Special Cases

$$|z|\ge0$$

$$|z|=0\Leftrightarrow z=0$$

For a real number $$a$$:

$$|a+0i|=|a|$$

## Usage

- Used to calculate the magnitude of a complex number.

- Forms the basis of Argand-plane and polar-form problems.