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The value of the expression (1+1/omega)...

The value of the expression `(1+1/omega)(1+1/omega^(2))+(2+1/omega)(2+1/omega^(2))+(3+1/omega^(2))+…………..+(n+1/omega)(n+1/omega^(2))`, where `omega` is an imaginary cube root of unity, is

A

`(n (n^(2)+ 2))/(3)`

B

`(n (n^(2)- 2))/(3)`

C

`(n(n^(2) + 1))/(3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • The value of the expression 1.(2 - omega) (2 - omega^(2)) + 2 (3 - omega) (3 - omega^(2))+…+ (n - 1). (n - omega) (n - omega^(2)) where omega is an imaginary cube root of unity, is

    A
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    B
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    C
    `(1)/(4) n^(2) (n + 1)^(2) + n`
    D
    none

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    A
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