Multiplication of Complex Numbers

Multiplication of Complex Numbers

## Formula

If:

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

then:

$$z_1z_2=(ac-bd)+i(ad+bc)$$

## Conditions / Special Cases

Using:

$$i^2=-1$$

the product becomes:

$$ac+iad+ibc+i^2bd=(ac-bd)+i(ad+bc)$$

## Usage

- Used in simplifying products and powers of complex numbers.