# Complex Power/Examples/2^i

## Example of Complex Power

$2^i = \map \cos {\ln 2} + i \map \sin {\ln 2}$

## Proof

 $\ds 2^i$ $=$ $\ds \map \exp {i \ln 2}$ Definition of Complex Power $\ds$ $=$ $\ds \map \cos {\ln 2} + i \map \sin {\ln 2}$ De Moivre's Formula

$\blacksquare$