Geometrical Interpretation of Multiplication

Geometrical Interpretation of Multiplication

## Formula

If:

$$z_1=r_1e^{i\theta_1},\qquad z_2=r_2e^{i\theta_2}$$

then:

$$z_1z_2=r_1r_2e^{i(\theta_1+\theta_2)}$$

## Interpretation

Multiplication of complex numbers:

- Multiplies their moduli.

- Adds their arguments.

## Usage

- Used to interpret complex multiplication as scaling and rotation in the Argand plane.