TITLE: How can you find the complex roots of i?
QUESTION [6 upvotes]: A variation of the Root of Unity problem.
I want to find all possible answers to this:
$$z^n = i$$
Where $$i^2 = -1$$

REPLY [2 votes]: Also, observe that if $z^n=i$ then $z^{4n}=1$. Thus, the complex numbers you're looking for are particular $4n$-th roots of $1$.
If you know that the $m$-th roots of 1 (any $m$) can be written as powers of a single well-chosen one (a primitive root), it shouldn't be too hardto find exactly which $4n$-th roots have the desired property.