JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

A value of

\theta

for which

\frac{2+3 i \sin \theta}{1-2 i \sin \theta}

is purely imaginary, is

View answer and explanation

Correct option: C

\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)

Option C (

\sin^{-1}(\frac{1}{\sqrt{3}})

) is correct because when the given expression is purely imaginary, its real part must be zero, leading to the equation

\sin^2 \theta = \frac{1}{3}

, which gives

\theta = \sin^{-1}(\frac{1}{\sqrt{3}})

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