JEE Mains · Maths · STD 11 - 4.1 complex nubers
A value of \(\theta\) for which \(\frac{{2 + 3isin\;\theta }}{{1 - 2i\sin \theta }}\) is purely imaginary, is:
- A \({\sin ^{ - 1}}\left( {\frac{{\sqrt 3 }}{4}} \right)\;\)
- B \(\;{\sin ^{ - 1}}\left( {\frac{1}{{\sqrt 3 }}} \right)\)
- C \(\frac{\pi }{3}\)
- D \(\;\frac{\pi }{6}\)
Answer & Solution
Correct Answer
(B) \(\;{\sin ^{ - 1}}\left( {\frac{1}{{\sqrt 3 }}} \right)\)
Step-by-step Solution
Detailed explanation
Purely imaginary means real part \(=0\) \( \frac{2+3 \sin \theta}{1-2 i \sin \theta} \times \frac{1+2 i \sin \theta}{1+2 i \sin \theta} \) \(=\frac{2+4 i \sin \theta+3 i \sin \theta-6 \sin ^{2} \theta}{1-(2 i \sin \theta)^{2}}\)…
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