Roots of Complex Polynomials 
Find all $x \in \mathbb{C}$ satisfying $(x - \sqrt{3} + 2i)^3 - 8i = 0$

I was able to find one value, $x = \sqrt{3} - 4i$.
I can also see that $x = -i$ also works although I am not able to devise a formal way for ending up with this value.
I am also unsure of how to find other values of $x$.

Hint: Divide your polynomial by $(x-(\sqrt{3} - 4i))$. You will get a quadratic polynomial. You found that $x = -i$ is also a root (great work!) so you should be to divide again by $(x+i)$. 
