Verified Solution • 2025–26 Session moderate

QJEEM22Ma12ff: JEE Main 2022 Mathematics - Class 11 JEEM22Ma12ff Solution: Let a circle C in complex plane pass through the points z 1 = 3 …

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 arg(z) is equal to :

Multiple Choice Options

  • A tan−1(25)−π
  • B tan−1(247)−π
  • C tan−1(3)−π
  • D tan−1(34)−π

Step-by-Step Verified Solution

z1=3+4i, z2=4+3i and z3=5i

Clearly, C≡x2+y2=25

Let z(x,y)

⇒(y−4x−3)(2−4)=−1

⇒y=2x−2≡L

∴ z is intersection of C & L

⇒z≡(−75,−245)

∴ Arg(z)=−π+tan−1(247)

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring