### Home > PC > Chapter 11 > Lesson 11.2.2 > Problem11-87

11-87.

Show that $i^{n}$ can be written as $\cos(\frac { n \pi } { 2 }) + i \sin (\frac { n \pi } { 2 })$.

Recall from problem 11-85 that $i$ can be written as:

Now use DeMoivre's theorem to write $i^{n}$.

$\textit{i}=\textit{z}=1\left( \cos\frac{\pi}{2}+\textit{i}\sin\frac{\pi}{2} \right)$