Finding complex roots of fourth degree polynomial $z^4 + 8z^3 + 16z^2 + 9$ I have the equation: $$z^4 + 8z^3 + 16z^2 + 9 = 0$$ 
I need to find all the complex solutions and I've got no clue how to approach it. I've tried factoring but nothing came out of it. I'm still very new to the world of complex numbers so I'll appreciate any help.

$$z^2(z+4)^2 =9i^2$$
so $$z^2+4z-3i=0\;\;\;\;{\rm or}\;\;\;\;z^2+4z+3i=0$$
You have a discriminant $D = 2(3+i)^2$ in the first case and $D = 2(3-i)^2$ in the second case.
