Complex Analysis 2

Algebra Level 4

(1+1ω)(1+1ω2)+(2+1ω)(2+1ω2)++(99+1ω)(99+1ω2)+(100+1ω)(100+1ω2) \large\left(1 + \frac1\omega\right)\left(1 + \frac1{\omega^2}\right) + \left(2 + \frac1\omega\right)\left(2 + \frac1{\omega^2}\right) + \ldots \\ \large + \left(99+ \frac1\omega\right)\left(99 + \frac1{\omega^2}\right)+ \left(100 + \frac1\omega\right)\left(100 + \frac1{\omega^2}\right)

Let ω\omega denote the complex cube root unity. Evaluate the summation above.

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