JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

Let

x = \alpha + \beta ,\;y = \alpha \omega + \beta {\omega ^2},\;z = \alpha {\omega ^2} + \beta \omega ,\;\omega

is an imaginary cube root of unity. The value of

xyz

View answer and explanation

Correct option: C

{\alpha ^3} + {\beta ^3}

Option C (

{\alpha ^3} + {\beta ^3}

) is correct because substituting the given expressions for

x, y, z

and using the properties of cube roots of unity simplifies the product

xyz

\alpha^3 + \beta^3

More Questions from COMPLEX NUMBERS

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{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

z, \frac{z}{1-z^2}

\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

a \neq 0

\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}