Question

Write the values of the square root of -i.

Answer 1

Let z = -i

$|z|=\sqrt{(0{)}^2+(-1{)}^2}=\sqrt{1}=1\text{Here x=0}andy=-1<0\therefore \sqrt{-i}=\pm \{\sqrt{\frac{1+0}{2}}-i\sqrt{\frac{1-0}{2}}\}(\because y<0)=\pm \{\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}}\}=\pm \frac{1}{\sqrt{2}}(1-i)$