AP EAMCET · Maths · Complex Number
The values of \(\theta\), for which \(\frac{3+2 i \sin \theta}{1-2 i \sin \theta}\) is real are
- A \(\theta=n \pi+\frac{\pi}{3}\) for \(n \in Z\)
- B \(\theta=n \pi+\frac{\pi}{4}\) for \(n \in Z\)
- C \(\theta=n \pi+\frac{\pi}{2}\) for \(n \in Z\)
- D \(\theta=n \pi\) for \(n \in Z\)
Answer & Solution
Correct Answer
(A) \(\theta=n \pi+\frac{\pi}{3}\) for \(n \in Z\)
Step-by-step Solution
Detailed explanation
\[ \begin{gathered} \frac{3+2 i \sin \theta}{1-2 i \sin \theta}=\frac{4}{1-2 i \sin \theta}-1 \\ =\frac{4(1+2 i \sin \theta)}{1+4 \sin ^2 \theta}-1 \end{gathered} \] which is real.…
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