JEE Main 2023MathematicsComplex NumberHardMCQ

JEE Main 2023 — Complex Number Question with Solution

JEE Main 2023 (25 Jan Shift 1)

Question

Let z1=2+3i and z2=3+4i. The set S=z∈C:z-z12-z-z22=z1-z22 represents a

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Show full solutionCorrect option: A
Correct answer
Astraight line with sum of its intercepts on the coordinate axes equals 14

Step-by-step explanation

Given,

z1=2+3i and z2=3+4i and the set

S=z∈C:z-z12-z-z22=z1-z22,

Now putting the value of z=x+iy, z1=2+3i and z2=3+4i in z-z12-z-z22=z1-z22 we get,

⇒(x-2)2+(y-3)2-(x-3)2-(y-4)2=1+1

⇒   x+y=7

Which is a straight line with intercept 7 on x & y axis, so sum of intercept will be 7+7=14.

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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.