Find the value of

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Analysis and Approaches · Number and Algebra · Number and Algebra

Problem

Find the value of

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

, where

i = \sqrt{-1}