There will be two answers on the complex plane. I have not worked them out yet.
This is my initial attempt to make sense of it:
\(\sqrt{-i}=\sqrt{-1}*\sqrt i=i*\sqrt i = i^\frac{3}{2}=(\sqrt{-1})^\frac{3}{2}=((-1)^\frac{1}{2})^\frac{3}{2}=(-1)^\frac{3}{4}\)
But wolframalpha says that one of the answer presentations is \(-(-1)^\frac{3}{4}\)
http://www.wolframalpha.com/input/?i=sqrt(-i)
So even my inital attempt is not correct
I do not where that negative sign out the front came from. ![]()