Question about the imaginary unit As we know, we define
$$\sqrt{-1}=i$$
But I always wondered, what about $\sqrt{i}$? As far as i can see, it is not an integer power of $i$. Every odd root has a solution in an integer power of $i$, but I can't find one for my question. Is there something I am missing here?

Consider $\frac{1+i}{\sqrt{2}}$. The square of this is $i$. It is a fact that the complex numbers are algebraically closed, and so in particular, every number has a square root.
