### Home > PC > Chapter 11 > Lesson 11.2.2 > Problem11-85

11-85.

Find the two square roots of $i$.

If you were to graph $i$ in the complex plane, it would be located at $\left(0, 1\right)$.What are the polar coordinates for the point $\left(0, 1\right)$?

$\textit{r} = 1, \theta=\frac{\pi}{2}, \textit{n}=2$

For $k = 0, 1$.

$\sqrt{1}\left( \cos \left( \frac{\frac{\pi}{2}+2k \pi}{2} \right) +i \sin \left( \frac{\frac{\pi}{2}+2k \pi}{2} \right) \right)$

$k = 0$

$\cos\frac{\pi}{4}+\textit{i}\sin\frac{\pi}{4}-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\textit{i}$

$k = 1$

$\sqrt{1}\left( \cos \left( \frac{\frac{\pi}{2}+2\pi}{2} \right) +i \sin \left( \frac{\frac{\pi}{2}+2 \pi}{2} \right) \right) \left( \cos \frac{5\pi}{4} + i \sin \frac{5\pi}{4} \right) ??$