JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Analyzing +4 | -1

The value of the expression

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

Where

\omega

is an imaginary cube root of unit is

View answer and explanation

Correct option: A

\left( {n - 1} \right)n\left( {{n^2} + 3n + 4} \right)/4

Option A is correct because the expression simplifies to

\frac{{(n - 1)n(n^2 + 3n + 4)}}{{4}}

after expanding and summing the terms using the properties of cube roots of unity.

More Questions from COMPLEX NUMBERS

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z \neq \pm 1

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\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

\left|\sum\limits_{r=1}^n z_r\right|

(z+a b)^3=a^3

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\alpha, \beta

\gamma

|\alpha-\beta|

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}