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

## Example of Use of Euler's Formula

$e^{i \pi / 2} = i$

## Proof

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

$\blacksquare$