Equality of Complex Numbers

Equality of Complex Numbers

## Definition / Concept

Two complex numbers are equal only when their real parts and imaginary parts are separately equal.

## Formula

If:

$$a+ib=c+id$$

then:

$$a=c$$

$$b=d$$

## Conditions / Special Cases

For:

$$z_1=a+ib,\qquad z_2=c+id$$

$$z_1=z_2\Leftrightarrow a=c\text{ and }b=d$$

## Usage

- Used to compare complex numbers and determine unknown real quantities.