# Euler's Formula/Examples/e^2 k i pi

## Example of Use of Euler's Formula

$\forall k \in \Z: e^{2 k i \pi} = 1$

## Proof

 $\ds e^{2 k i \pi}$ $=$ $\ds \cos 2 k \pi + i \sin 2 k \pi$ Euler's Formula $\ds$ $=$ $\ds 1 + i \times 0$ Cosine of Multiple of $\pi$, Sine of Multiple of $\pi$ $\ds$ $=$ $\ds 1$

$\blacksquare$