JEE Mains · Maths · STD 11 - 4.1 complex nubers
The sum of all possible values of \(\theta \in[-\pi, 2 \pi]\), for which \(\frac{1+i \cos \theta}{1-2 i \cos \theta}\) is purely imaginary, is equal to
- A \(2 \pi\)
- B \(3 \pi\)
- C \(5 \pi\)
- D \(4 \pi\)
Answer & Solution
Correct Answer
(B) \(3 \pi\)
Step-by-step Solution
Detailed explanation
\( Z=\frac{1+i \cos \theta}{1-2 i \cos \theta} \) \( Z=-\bar{Z} \Rightarrow \frac{1+i \cos \theta}{1-2 i \cos \theta}=-\left(\frac{\overline{1+i \cos \theta}}{1-2 i \cos \theta}\right) \)…
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