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The value of sum (k = 1)^(6) ( sin "" (...

The value of ` sum _(k = 1)^(6) ( sin "" ( 2 pi k)/( 7) - i cos "" ( 2 pi k)/( 7))` is

A

`-1`

B

0

C

`-i`

D

`i`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • The value of sum _(i = 1) ^(10) ( sin "" ( 2 k pi)/(11) + i cos "" (2 k pi)/( 11)) is

    A
    1
    B
    `-1`
    C
    0
    D
    i

  • The value of sum _( k =1) ^( 6) (( sin 2 kpi k )/( 7) - ( icos 2pi k )/( 7)) is

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    `-1`
    B
    0
    C
    `-i`
    D
    `i`

  • The value of 1 + sum _(k = 0)^( 12) { cos "" (( 2 k + 1) pi)/( 13) + i sin "" (( 2 k + 1) pi)/( 13)} is

    A
    0
    B
    `-1`
    C
    1
    D
    i

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