Ain't these 11th roots of unity ?

Algebra Level 4

k=110[sin(2kπ11)icos(2kπ11)]= ?\displaystyle \sum_{k=1}^{10}\left[ \sin\left(\frac{2k\pi}{11}\right)-i\cos\left(\frac{2k\pi}{11}\right)\right]=\ ?

Note: i=1i=\sqrt{-1}


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