JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Hard

1 of 1

Application +4 | -1

1, \omega, \omega^2, \ldots, \omega^{n-1}

are the

n, n

th roots of unity and

z_1, z_2

are any two complex numbers, then

\sum_{k=0}^{n-1}\left|z_1+\omega^k z_2\right|^2

is equal to

View answer and explanation

Correct option: A

n\left[\left|z_1\right|^2+\left|z_2\right|^2\right]

Option A (

n[|z_1|^2+|z_2|^2]

) is correct because it is derived from expanding the sum and using the properties of nth roots of unity.

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