JEE Main 2013MathematicsComplex NumberHardMCQ

JEE Main 2013 — Complex Number Question with Solution

JEE Main 2013 (07 Apr)

Question

If z is a complex number of unit modulus and argument θ, then arg 1+z1+z- can be equal to given z≠-1

Choose an option

Show full solutionCorrect option: A
Correct answer
A θ

Step-by-step explanation

Let z=cos θ+i sin θ

Then, 1+z1+z¯=1+cos θ+i sin θ1+cos θ-i sin θ

=2 cos2θ2+i·2 sinθ2cosθ22 cos2θ2-i·2 sinθ2cosθ2

=cosθ2+i sinθ2cosθ2-i sinθ2

=cosθ2+i sinθ22

=cos θ+i sin θ

∴   arg1+z1+z¯=arg z

=θ

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About this question

This is a previous-year question from JEE Main 2013, 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.