JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

a = \cos \frac{{4\pi }}{3} + i\sin \frac{{4\pi }}{3},

then the value of

{\left( {\frac{{1 + a}}{2}} \right)^{3n}}

View answer and explanation

Correct option: B

\frac{{{{\left( { - 1} \right)}^n}}}{{{2^{3n}}}}

Option B (

\frac{{{{\left( { - 1} \right)}^n}}}{{{{2^{3n}}}}}

) is correct because it is the simplified form of the given expression using trigonometric identities and De Moivre's theorem.

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