# 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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