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I need this result to compute a residue. I haven't been successful so far.

What I have tried: I have tried decomposing $\frac{1}{z^2 - z + 1} = \frac{A + Bi}{z - \omega} + \frac{C + Di}{z + \omega}$ where $\omega$ is the cube root of unity. I didn't get anything from this method.

3 Answers 3