JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Hard

1 of 1

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)^{3 n}

View answer and explanation

Correct option: B

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

Option B (

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

) is correct because after simplification using trigonometric identities and De Moivre's theorem, the expression equals

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

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