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The value of the expression 1.(2-omega)....

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

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

B

`(1)/(4) n^(2) (n + 1)^(2) - n`

C

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

D

none

Text Solution

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The correct Answer is:
B
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Knowledge Check

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

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    B
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    C
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    D
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    A
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    D
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