# Complex Indeed!

Algebra Level 5

$\displaystyle \large \sum_{p=1}^{32} (3p+2) \left [ \sum_{q=1}^{10} \left ( \sin \left ( \frac {2\pi q}{11} \right ) - i \cos \left ( \frac {2\pi q}{11} \right ) \right ) \right ]^p$

I have a summation within a summation in the above expression. What is its value?

Details and Assumptions:

$$i$$ is an imaginary number such that $$i^2 = -1$$

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