Geometrical Interpretation of Division

Geometrical Interpretation of Division

## Formula

If:

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

then:

$$\frac{z_1}{z_2}=\frac{r_1}{r_2}e^{i(\theta_1-\theta_2)}$$

## Interpretation

Division of complex numbers:

- Divides their moduli.

- Subtracts their arguments.

## Usage

- Used to interpret division geometrically and solve argument-based problems.