z1≡A≡(3,4),z2≡B≡(4,3),z3≡C≡(0,5)
and z≡P≡(x,y)
Slope of BC=4−03−5=−21
Slope of AP=2
Now, equation of APisy−4=2(x−3)
⇒y=2(x−1)
Since P lies on circle x2+y2=25
⇒x2+(2(x−1))2=25
⇒x=−57 and y=−524
⇒arg(z)=tan−1(724)−π
JEE Main 2022 — Mathematics Algebra
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
Held on 25 Jun 2022 · Verified 6 Jul 2026.
tan−1(724)−π
tan−1(52)−π
tan−1(3)−π
tan−1(43)−π
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