A) 1
B) -1
C) \[-i\]
D) \[i\]
Correct Answer: C
Solution :
\[\sum\limits_{k=1}^{10}{\left( \sin \frac{2k\pi }{11}+i\cos \frac{2k\pi }{11} \right)}\] \[=i\sum\limits_{k=1}^{10}{\left( \cos \frac{2k\pi }{11}+i\sin \frac{2k\pi }{11} \right)}\] \[=i\,\sum\limits_{k=1}^{10}{\left( {{e}^{-\frac{2k\pi }{11}}} \right)}\] \[=i\,\left\{ \sum\limits_{k=0}^{10}{\left( {{e}^{-\frac{2k\pi }{11}}} \right)-1} \right\}\] \[=-i\]
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