Argument Properties

Argument Properties

## Formula

$$\arg(z_1z_2)=\arg(z_1)+\arg(z_2)$$

$$\arg\left(\frac{z_1}{z_2}\right)=\arg(z_1)-\arg(z_2)$$

$$\arg(z^n)=n\arg(z)$$

$$\arg(\bar z)=-\arg(z)$$

$$\arg\left(\frac1z\right)=-\arg(z)$$

## Conditions / Special Cases

These relations are understood modulo:

$$2\pi$$

For principal arguments, the resulting angle may need to be adjusted to the principal range.

## Usage

- Used to determine arguments of products, quotients, powers and conjugates.