Find the square root of the following complex number: `-i`

Explanation

Let `z=-i`

`abs(z)=abs(-i)=abs(-1) xx abs(i)`

`abs(z)=1`

`sqrt(-i)=+-[sqrt(frac{abs(z)+Re(z)}{2})-isqrt(frac{abs(z)+Re(z)}{2})]`

`=sqrt(-i)=+-[sqrt(frac{1+0}{2})-isqrt(frac{1-0}{2})`

`=sqrt(-i)=+-[sqrt(frac{1}{2})-isqrt(frac{1}{2})`

`=+-frac{1}{sqrt(2)}(1-i)`