If $\alpha $ is a cube root of unit and is not real, then ${{\rm{\alpha }}^{3n + 1}} + {{\rm{\alpha }}^{3n + 3}} + {{\rm{\alpha }}^{3n + 5}}$ has the value

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

\alpha

is a cube root of unit and is not real, then

{\mathrm{\alpha }^{3n + 1}} + {\mathrm{\alpha }^{3n + 3}} + {\mathrm{\alpha }^{3n + 5}}

has the value

View answer and explanation

Correct option: B

Option B (0) is correct because substituting

\alpha = \omega

and using the properties of cube roots of unity (

\omega^3 = 1

and

1 + \omega + \omega^2 = 0

) simplifies the expression to 0.

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