Complex Number in Cartesian Form

Complex Number in Cartesian Form

## Formula

$$z=x+iy$$

If:

$$z=r(\cos\theta+i\sin\theta)$$

then:

$$x=r\cos\theta$$

$$y=r\sin\theta$$

and:

$$r=\sqrt{x^2+y^2}$$

## Conditions / Special Cases

$$x=\operatorname{Re}(z)$$

$$y=\operatorname{Im}(z)$$

$$r=|z|$$

## Usage

- Used to convert between Cartesian and polar representations.