Answer
Ans. $\frac{1}{√2}+\frac{i}{√2}$, $\frac{-1}{√2}+\frac{-i}{√2}$
Work Step by Step
Given:- z=i
$ z^{1/2}=i^{1/2}$
As we can write i=$cosπ/2+isinπ/2$
$ z^{1/2}=[cos{(\frac{π}{2}+{2πk})}+isin({\frac{π}{2}+{2πk})}]$
After putting k=0, 1
We get
= $cos\frac{π}{4}+isin\frac{π}{4}$,$cos\frac{5π}{4}+isin\frac{5π}{4}$
=$\frac{1}{√2}+\frac{i}{√2}$, $\frac{-1}{√2}+\frac{-i}{√2}$
Ans.
