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Find the sum 1xx(2-omega)xx(2-omega^(2))...

Find the sum `1xx(2-omega)xx(2-omega^(2))+2xx(-3-omega)xx(3-omega^(2))+….+(n-1)xx(n-omega)xx(n-omega^(2))`, where `omega` is an imaginary cube root of unity.

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
A
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