JEE Mains · Maths · STD 11 - 4.1 complex nubers
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
- A \(\frac{1}{2}(\sqrt{3}-i)\)
- B \(-\frac{1}{2}(\sqrt{3}-i)\)
- C \(-\frac{1}{2}(1-i \sqrt{3})\)
- D \(\frac{1}{2}(1-i \sqrt{3})\)
Answer & Solution
Correct Answer
(B) \(-\frac{1}{2}(\sqrt{3}-i)\)
Step-by-step Solution
Detailed explanation
The value of \(\left(\frac{1+\sin 2 \pi / 9+i \cos 2 \pi / 9}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)\)…
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