More Fun in 2015, Part 40

Algebra Level 4

Compute \[S=\sum\frac{1}{(1-\omega)^{2015}}\]

where the sum is taken over all \(2015^\text{th} \) roots of unity \(\omega\) with \(\omega\neq 1\).


Inspiration.

Enjoy it while it lasts; this problem will become a lot harder next year!
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