Question

${\sum }_{k=1}^6[\sin \frac{2k\pi }{7}-\iota \cos \frac{2k\pi }{7}]=$

• A. -1
• B. 0
• C. $-\iota$
• D. $\iota$

Answer 1

The correct option is D $\iota$

$-\iota {\sum }_{k=1}^6\left[cos\frac{2k\pi }{7}+\iota sin\frac{2k\pi }{7}\right]$
$-\iota [{1+\alpha +\alpha }^2+...+{\alpha }^6-1]=-\iota [0-1]=\iota$