Find all numbers $z \in \mathbb{C}$ such that $(z−i)^5 = \sqrt{3} +i$ This is a follow-up question to finding all solutions for $z \in \mathbb{C}$ such that $z^5 = \sqrt{3} +i$ but I have no idea how to approach this question (might just be having a brain fart)
The only way I can think of solving it would be to expand it into a polynomial and then solve for z but that seems like a lot more work than necessary, and I would think this answer would have something to do with my answer to the previous question.

Hint:
Write $\sqrt 3+i$ in exponential form., and you'll find out it's a problem of finding the $5$th roots of a complex number with modulus $1$.
