Question

The value of $\sum _{k=1}^{10}$$(sin\frac{2k\pi }{11}-icos\frac{2k\pi }{11})$ is

• A. -i
• B. i
• C. 1
• D. -1

Answer 1

The correct option is B

i

$\sum _{k=1}^{10}$$(sin\frac{2k\pi }{11}-icos\frac{2k\pi }{11})$ = -i$\sum _{k=1}^{10}$$(cos\frac{2k\pi }{11}-isin\frac{2k\pi }{11})$ = -i $(1+\sum _{k=1}^{10}cos\frac{2k\pi }{11}+isin\frac{2k\pi }{11}-1)$ = i