One of the $15^{ ext {th }}$ roots of -1 is

Question

One of the $15^{	ext {th }}$ roots of -1 is

Aicharya · Accepted Answer

$\begin{aligned} & 	ext {Since }(-1)^{1 / 15}=(-\cos 2 \pi+i \sin 2 \pi)^{1 / 15} \ & =\left(-\cos \frac{2 \pi}{15}+i \sin \frac{2 \pi}{15}ight)=\cos \left(\frac{13 \pi}{15}ight)+i \sin \left(\frac{13 \pi}{15}ight) \ & =\operatorname{cis}\left(\frac{13 \pi}{15}ight)\end{aligned}$

One of the $15^{\text {th }}$ roots of -1 is

Solution