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# help

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Let $$\omega$$ be a nonreal root of $$z^3 = 1.$$ Let $$a_1,$$ $$a_2,$$ $$\dots,$$ $$a_n$$ be real numbers such that $$\frac{1}{a_1 + \omega} + \frac{1}{a_2 + \omega} + \dots + \frac{1}{a_n + \omega} = 2 + 5i.$$ Compute $$\frac{2a_1 - 1}{a_1^2 - a_1 + 1} + \frac{2a_2 - 1}{a_2^2 - a_2 + 1} + \dots + \frac{2a_n - 1}{a_n^2 - a_n + 1}.$$

Apr 5, 2019