determine the complex solutions of the equation

Question

(z+4)³ = -8i

Answer 1

By taking the 3rd root we obtain that z+4=2(-i)^(1/3)=2 e^(iπ/2) or 2 e^(-iπ/6) or 2 e^(-5iπ/6) from where we arrive at the three solutions of the equation. This happens because we have three 3rd roots of -i.