Complex Analysis 2

Algebra Level 4

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

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