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## Homework Statement

Find all complex solutions of z^6 + z^3 + 1

(z^3 + 1)/(z^3 - 1) = i

## Homework Equations

## 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?