This should be the easiest part of my module but i just cant figure it out

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Let $\displaystyle f(z) = \frac{e^{2 i \pi z}}{1 + z^3}$. Find the singularities and classify them.

So need to find $\displaystyle z$ when $\displaystyle z^3 = -1$.

One root is -1. The others we get from DeMoivres Thm...

I seem to think it should be something like $\displaystyle z = \cos(\frac{k \pi}{3}) + i\sin(\frac{k \pi}{3})$ for k = 1,2,3 but that gets me $\displaystyle i \frac{\sqrt(3)}{2} \pm \frac{1}{2}$ instead of $\displaystyle \frac{1}{2} \pm i \frac{\sqrt(3)}{2}$...