The value of 3 2 2 1 sin cos 9 9 2 2 1 sin cos 9 9 i i æ ö p p + + ç ÷ p p + – è ø is :

Question:

The value of $\left(\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)^{3}$ is

  1. $\frac{1}{2}(1-i \sqrt{3})$

  2. $\frac{1}{2}(\sqrt{3}-i)$

  3. $-\frac{1}{2}(\sqrt{3}-i)$

  4. $-\frac{1}{2}(1-i \sqrt{3})$

Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Complex Numbers and Quadratic Equations chapter.
JEE Main Previous Year Sep. 02, 2020 (I)

Solution:

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