JEE Main 2019MathematicsComplex NumberEasyMCQ

JEE Main 2019 — Complex Number Question with Solution

JEE Main 2019 (09 Jan Shift 1)

Question

Let A=θ∈-π2,π:3+2i sinθ1-2i sinθ is purely imaginary . Then the sum of the elements in A is:

Choose an option

Show full solutionCorrect option: C
Correct answer
C2π3

Step-by-step explanation

Given complex number is z=3+2isinθ1-2isinθ

⇒z=(3+2isinθ)(1+2isinθ)(1+4sin2θ)

Since given complex number is purely imaginary

⇒Re(z)=0

⇒3-4sin2θ=0

⇒sinθ=±32

⇒θ=-π3,π3,2π3

⇒ sum of all possible values of θ=2π3 .

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About this question

This is a previous-year question from JEE Main 2019, 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.