JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

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Application +4 | -1

\omega

is an imaginary cube root of unity and

x = a + b,\;y = a\omega + b{\omega ^2},\;\;z = a{\omega ^2} + b\omega

, then

{x^2} + {y^2} + {z^2}

is equal to

View answer and explanation

Correct option: A

6ab

Option A (

6ab

) is correct because after substituting the given values of x, y, and z and simplifying using the properties of cube roots of unity, the expression

{x^2} + {y^2} + {z^2}

reduces to

6ab

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