JEE Main 2023MathematicsComplex NumberEasyMCQ

JEE Main 2023 — Complex Number Question with Solution

JEE Main 2023 (08 Apr Shift 2)

Question

Let A=θ∈0, 2π:1+2isinθ1-isinθ is purely imaginary Then the sum of the elements is in A is

Choose an option

Show full solutionCorrect option: A
Correct answer
A4π

Step-by-step explanation

Let

z=1+2isinθ1-isinθ

⇒z=1+2isinθ1-isinθ×1+isinθ1+isinθ

⇒z=1-2sin2θ+3isinθ1+sin2θ

⇒z=1-2sin2θ1+sin2θ+i3sinθ1+sin2θ

Since, z is a purely imaginary number, so real part must be zero, hence

1-2sin2θ1+sin2θ=0

⇒1-2sin2θ=0

⇒cos2θ=0

⇒θ=π4,3π4,5π4,7π4, for θ∈0,2π

∴Sum of all values =16π4=4π

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About this question

This is a previous-year question from JEE Main 2023, 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.