How do I solve: $$ e^{4z}+e^{3z}+e^{2z}+e^z+1=0 $$
I'm getting lost on where to start. I tried using the definition $$ e^z=e^x(\cos(y) +i\sin(y)) $$
But that doesn't seem to do me any good. I also tried using complex powers, but I seem to just be going in circles. Any suggestions?
