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The value of underset(k=1)overset(6)(sin...

The value of `underset(k=1)overset(6)(sin (2 pi k)/(7) = I cos (2 pi k )/(7)` is

A

-1

B

0

C

`-i`

D

I

Text Solution

Verified by Experts

The correct Answer is:
D
`(underset(k=1)overset(6)Sigmasin"" (2kpi)/7-i cos ""(2kpi)/7)`
`=underset(k=1)overset(6)Sigma-i (cos""(2kpi)/7+sin""(2kpi)/7)`
`=i{underset(k=1)overset(6)Sigma-i`
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