Q:

Solve the complex equation

The equation is $$z^2 -4z +4+ 2i = 0$$ 
I know that i am supposed to use $$(a+bi)^2 = a^2 + 2abi + bi^2$$ to solve the equation but i am stuck on how to expand the equation. 
Can you help out with which term to expand? 

A:

Hint: Since $z^2-4z+4 = (z-2)^2$, we can write this equation as $(z-2)^2+2i = 0$. 
This gives you $(z-2)^2 = -2i$. Can you find the two square roots of $-2i$?