JEE Main 2020MathematicsComplex NumberHardMCQ

JEE Main 2020 — Complex Number Question with Solution

JEE Main 2020 (07 Jan Shift 1)

Question

If Rez-12z+i=1, where z=x+iy, then the point x,y lies on a

Choose an option

Show full solutionCorrect option: D
Correct answer
Dcircle whose diameter is 52

Step-by-step explanation

Let z=x+iy
z-12z+i=x-1+iy2x+iy+i=x-1+iy2x+2y+1i×2x-2y+1i2x-2y+1i
Rez+12z+i=2xx-1+y2x+12x2+2y+12=1
⇒2x2+2y2-2x+y=4x2+4y2+4y+1
⇒2x2+2y2+2x+3y+1=0
⇒x2+y2+x+32y+12=0

Circle with center -12, -34
r=14+916-12=4+9-816=54 ⇒ d=52

where, d=diameter of the given circle.

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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.