Imaginary number challenge

Algebra Level 4

\[\large \sum_{k=1}^{2016} \left(\left(\frac{k-i}{i-k}\right)^{k} \times \frac{k}{i^k} \times i^{2016k} \right)= a-bi\]

If the above equation is true for positive integers \(a\) and \(b\), find \(a+b\).

Clarification: \(i=\sqrt{-1}\).

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