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140
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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
 #1
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The answer is 14.

 Nov 30, 2019

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