If $x = a + b,\;y + a\alpha + b\beta \;\,{\rm{and\;}}\,{\rm{z}} = a\beta + b\alpha ,\;\,{\rm{where}}\,\;\alpha \,\;{\rm{and}}\;\beta $ are complex cube roots of unity, then $xyz$ is equal to

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

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Application +4 | -1

x = a + b,\;y + a\alpha + b\beta \;\,\mathrm{and\;}\,\mathrm{z} = a\beta + b\alpha ,\;\,\mathrm{where}\,\;\alpha \,\;\mathrm{and}\;\beta

are complex cube roots of unity, then

xyz

is equal to

View answer and explanation

Correct option: B

{a^3} + {b^3}

The correct answer is B (

{a^3} + {b^3}

) because it is obtained by multiplying the given expressions and using the properties of complex cube roots of unity.

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