De Moivre's Theorem

Theorem

If $\forall n>0$ Then $z^n=r^n{e}^{in\theta }$

Writing $\sqrt{i}$ in standard form

$\sqrt{i}=\sqrt{e^{i\frac{\pi }{2}}}$ = ${\left(e^{i\frac{\pi }{2}}\right)}^{\frac{1}{2}}$ = $(e^{i\frac{\pi }{4}})$ = $\cos (\frac{\pi }{4})+i\sin (\frac{\pi }{4})$ = $\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}$