Question: I have tried to solve the following equation:

$$
(z+1)^4+4(z-1)^4=0 \quad,\quad z=(a+bi)
$$

If I could leave the $z^4$ alone I could solve it using the formula, but I do not know how to operate with it having additions and substractions. 

Can someone please help me?
Thank you!

Answer: 
What would you do if you had
$$
(z+1)^4-4(z-1)^4=0
$$
instead? You'd observe it is
$$
((z+1)^2-2(z-1)^2)((z+1)^2+2(z-1)^2)=0
$$
Well, with $+$ you can write it as
$$
(z+1)^4-(2i)^2(z-1)^4=0
$$
Can you factor $(z+1)^4 + 4(z-1)^4$ (or perhaps an equivalent form of this) into the product of two quadratics? (Hint: Yes)