JEE Main 2022MathematicsComplex NumberMediumMCQ

JEE Main 2022 — Complex Number Question with Solution

JEE Main 2022 (25 Jun Shift 1)

Question

Let a circle C in complex plane pass through the points z1=3+4i,z2=4+3i and z3=5i. If z≠z1 is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then argz is equal to

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Show full solutionCorrect option: A
Correct answer
Atan-1247-π

Step-by-step explanation

z1≡A≡3,4, z2≡B≡4,3, z3≡C≡0,5

and z≡P≡x,y

Slope of BC=3-54-0=-12

Slope of AP=2

Now, equation of AP is y-4=2x-3

⇒y=2x-1

Since P lies on circle x2+y2=25

⇒x2+2x-12=25

⇒x=-75 and y=-245

⇒arg(z)=tan-1247-π

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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.