Question

Use DeMoivre's Theorem to find the following. Write your answer in standard form.

(sqrt2 cis 9pi/20)^5

Answer 1

@ProHeIper

Answer 2

\[\left(\sqrt2~\mathrm{cis}\,\frac{9\pi}{20}\right)^5=(\sqrt2)^5~\mathrm{cis}\,\frac{45\pi}{20}=\cdots \]
since DeMoivre's theorem says that
\[(\mathrm{cis}\,t)^n=\mathrm{cis}\,nt\]