JEE Main 2023MathematicsComplex NumberHardNumerical

JEE Main 2023 — Complex Number Question with Solution

JEE Main 2023 (30 Jan Shift 1)

Question

Let z=1+i and z1=1+iz¯z¯(1-z)+1z· Then 12π argz1 is equal to

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Show full solutionCorrect answer: 9
Correct answer
9

Step-by-step explanation

Given:

z=1+i

z¯=1-i

And, 1z=11+i×1-i1-i=1-i2

So,

z1=1+iz¯z¯(1-z)+1z

=1+i-i2(1-i)(-i)+1-i2

=1+i-i2-i+i2+12-i2

=2+i-3i-12=4+2i-3i-1

=-(4+2i)(3i-1)(3i)2-(1)2

=12i-4+6i2-2i10

=10i-1010=i-1

Argz1=3π4

∴12πargz1=12π×3π4=9

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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.