JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

The value of the expression

1(2-\omega)\left(2-\omega^2\right)+2(3-\omega)\left(3-\omega^2\right)+\ldots .+(n-1)

(n-\omega)\left(n-\omega^2\right)

, where

\omega

is an imaginary cube root of unity, is

View answer and explanation

Correct option: B

\left(\frac{n(n+1)}{2}\right)^2-n

Option B (

\left(\frac{{n(n+1)}}{{2}}\right)^2-n

) is correct because the given expression can be simplified to a sum of cubes minus a linear term, which results in the given expression.

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