Euler's Formula

Euler's Formula

## Formula

$$e^{i\theta}=\cos\theta+i\sin\theta$$

Therefore:

$$z=re^{i\theta}$$

## Conditions / Special Cases

For $\theta=\pi$:

$$e^{i\pi}=-1$$

Hence:

$$e^{i\pi}+1=0$$

## Usage

- Used to convert between polar and exponential forms of a complex number.

- Forms the basis of De Moivre's theorem.