Question

Calculate $\sqrt{i}$

Answer 1

$z=i=r{e}^{i\theta }$(let)

$r=\sqrt{1+0}=1$

$\theta ={\tan }^{-1}\left(\frac{1}{0}\right)=\pi /2$

$z=e^{i\pi /2}$

$z^2=e^{i\pi /4}$

$⟹(\cos \pi /4+i\sin \pi /4)$

$⟹\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}$