JEE Main 2016MathematicsComplex NumberMediumMCQ

JEE Main 2016 — Complex Number Question with Solution

JEE Main 2016 (03 Apr)

Question

A value of θ for which 2+3isinθ1-2isinθ is purely imaginary, is

Choose an option

Show full solutionCorrect option: B
Correct answer
Bsin-113

Step-by-step explanation

Let, z=2 + 3isin θ1 - 2isin θ

Multiplying the denominator by its conjugate, we get,

z=2+3 isin θ 1+2 isin θ1+4 sin2 θ

=2-6 sin2 θ+i7sin θ1+4 sin2 θ

To make it purely imaginary. Its real part should be 0.

Hence, 2=6 sin2⁡θ

⇒sin⁡θ=±13

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About this question

This is a previous-year question from JEE Main 2016, covering the Complex Number chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.