Jamya Elliott

2022-01-31

How do I find the square roots of i?

Jordyn Horne

Expert

Step 1
Let $z=r{e}^{ithere}$ be the square-roots of i.
${z}^{2}=i⇒{r}^{2}{e}^{i\left(2\theta \right)}={e}^{i\left(\frac{\pi }{2}+2n\pi \right)}$
$⇒\left\{\begin{array}{l}{r}^{2}=1⇒r=1\\ 2\theta =\frac{\pi }{2}+2n\pi ⇒\theta =\frac{\pi }{4}+n\pi \end{array}$

Do you have a similar question?