Reciprocal of a Complex Number

Reciprocal of a Complex Number

## Formula

For:

$$z=a+ib,\qquad z\ne0$$

$$\frac1z=\frac{\bar z}{|z|^2}$$

Therefore:

$$\frac1{a+ib}=\frac{a-ib}{a^2+b^2}$$

## Conditions / Special Cases

$$z\ne0\Leftrightarrow a^2+b^2\ne0$$

## Usage

- Used to simplify reciprocal expressions and complex-number divisions.