How to find all complex numbers and roots of z in cubic equations

Question

I am having difficulty solving complex number questions involving cubic roots an example of one such question is written below:

How to find all complex numbers and roots of $z$ such that $z^3+4iz=0$?

Any help or clarification would be highly appreciated!

Answer 1

Hint: $z^3+4iz=0\iff z(z^2+4i)=0$