## Corollary 1.2.15: DeMoivre's Theorem |

For any integer |

DeMoivre's Formula is quite something. It says that if you take a number
on the unit circle (i.e. with lenght 1) with initial argument (angle) *t*
and multiply it by itself, it simply rotates around the unit circle by that
angle *t*. Each time you multiply the number by itself, the
vector rotates another *t* degrees. In other words, in this case
the power operator results in a simple rotation.

Powers of a vectorzwith|z|=1

The proof of the formula follows directly from our previous theorem on
multiplying directly. We showed that if *z = r cis(t)*
then *z ^{n} = r^{n} cis(nt)*. Now let

[ x ]