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If omega is a complex cube root of unity...

If `omega` is a complex cube root of unity, then the value of the expression `1(2-omega)(2-omega^2)+2(3-omega)(3-omega^2) +...+(n-1) (n-omega)(n-omega^2) (n>=2) ` is equal to (A) `(n^2(n+1)^2)/4 - n` (B) `(n^2(n+1)^2)/4 +n` (C) `(n^2(n+1))/4 -n` (D) `(n(n+1)^2)/4 -n`

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If omega is an imaginary cube root of unity, then the value of (2 - omega )(2 - omega^(2) ) + 2(3 - omega )(3 - omega^(2)) + .... .... + (n - 1)(n - omega)(n -omega^(2)) is

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

  • If omega is a complex cube root of unity, then for positive integral value of n, the product of omega.omega^2.omega^3...omega^n will be

    A
    `(1-lsqrt3)/2`
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    B
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