JEE Main 2020MathematicsComplex NumberMediumMCQ

JEE Main 2020 — Complex Number Question with Solution

JEE Main 2020 (04 Sep Shift 1)

Question

Let u=2z+iz-ki,z=x+iy and k>0. If the curve represented byRe(u)+Im(u)=1 intersects the y-axis at points P and Q where PQ=5 then the value of k is

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Show full solutionCorrect option: D
Correct answer
D2

Step-by-step explanation

u=2x+iy+ix+iy−k i=2x+2y+1ix+y−ki×x−y−kix−y−ki

Real part of u=Reu=2x2+2y+1y−kx2+y−k2

Imaginary part of u=Imux2y+1−2xy−kx2+y−k2

Now Reu+Imu=1

2x2+2y+1y−k+x2y+1−2xy−kx2+y−k2=1

for y-axis put x=0

⇒ 2y+1y−ky−k2=1

⇒ y−ky+1+k=0

y=k, −1+k

Now point P0, k, Q0, −1+k

PQ=2K+1=5

2k+1=±5

2k=4,−6

k=2,−3

Hence, k=2   k>0.

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About this question

This is a previous-year question from JEE Main 2020, 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.