I need to find all the solutions to the following using logarithms:
$(e^z-1)^3=1$ where z is a complex number.
I am told that using roots of unity I can break this equation down but I must be missing something.
So far...
$c=e^z-1$
$c^3=1$
$c=1^{1/3}e^{i(2 π k/3)}$ ; $k={0,1,2}$
$e^z-1=1^{1/3}e^{i(2 π k/3)}$
And from there I'm stuck, assuming I'm actually making progress. A hint would be swell.