JEE Main 2022MathematicsComplex NumberMediumNumerical

JEE Main 2022 — Complex Number Question with Solution

JEE Main 2022 (28 Jun Shift 2)

Question

Sum of squares of modulus of all the complex numbers z satisfying z¯=iz2+z2-z is equal to

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

Given,

z+z¯=izz2+z2

Consider z=x+iy

2x=i+1x2-y2+2xyi

On comparing real and imaginary part we get,

⇒2x=x2-y2-2xy and x2-y2+2xy=0

⇒2x=-4xy

⇒ x=0 or y=-12

Case 1: x=0⇒2×0=i+102-y2+2×0×yiy=0 

Here z=0

Case 2: y=-12

⇒4x2-4x-1=0

2x-12=2

2x-1=±2

x=1±22

Here z=1+22-i2 or z=1-22-i2

Sum of squares of modulus of z

=0+1+22+14+1-22+14=84=2

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About this question

This is a previous-year question from JEE Main 2022, 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.