What is $\sqrt i^i $?

Question

my answer would be $i$ because I used the definition $i=\sqrt-1$ and replaced the $i$ with that

I'm not sure if I got it right though

Answer 1

$$\sqrt{i}^i=i^{i/2}=\exp \left(\left(\dfrac{\pi i}{2}+2\pi i n\right)\cdot \dfrac{i}{2}\right)=\exp \dfrac{-\pi}{4}\cdot\exp-\pi n, \ n\in \mathbb{Z}$$