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Let \(\omega\) be a complex number such that \(\omega^5\) and \(w \neq 1\). Compute \(\frac{\omega}{1 + \omega^2} + \frac{\omega^2}{1 + \omega^4} + \frac{\omega^3}{1 + \omega} + \frac{\omega^4}{1 + \omega^3}.\)

 

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 Jan 17, 2021
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One possible value of w is -0.587785i - 0.782431.  Pluggins this in, we get that the vaue of the expression is -1.

 Jan 18, 2021

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