JEE Main 2021MathematicsComplex NumberHardNumerical

JEE Main 2021 — Complex Number Question with Solution

JEE Main 2021 (26 Feb Shift 2)

Question

Let z be those complex numbers which satisfy z+5≤4 and z1+i+z¯1-i⩾-10,i=-1. If the maximum value of |z+1|2 is α+β2, then the value of α+β is

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Show full solutionCorrect answer: 48
Correct answer
48

Step-by-step explanation

Let z=x+iy

Given |z+5|≤4

x+52+y2≤16  ...1

z1+i+z¯1-i≥-10

z+z¯+iz-z¯≥-10

x-y+5≥0   ...2

|z+1|2=|z--1|2

Let P-1,0

|z+1|Max.2=PB2 (where B is in 3rd quadrant) 

for point of intersection 

x+52+y2=16x-y+5=0y=±22

A22-5,22 B-22-5,-22

PB2=+22+42+222

|z+1|2=8+16+162+8

α+β2=32+162

α=32,β=16⇒α+β=48

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About this question

This is a previous-year question from JEE Main 2021, 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.