Find all complex solutions of z^6 + z^3 + 1
(z^3 + 1)/(z^3 - 1) = i
The Attempt at a Solution
I am going crazy with trial and error with these, there must be some systematic method or tricks that I am oblivious of. For the second question I factored it to:
[(z+1)(z^2 - z + 1)]/[(z-1)(z^2 + z +1)] = i
obviously we have conditions z cannot equal 1. But also z cannot = -1/2 +- sqrt(3)i What happens here?