Let a circle C in complex plane pass through the points $z_{1} = 3 + 4 i, z_{2} = 4 + 3 i$ and $z_{3} = 5 i$ . If $z (\neq z_{1})$ is a point on C such that the line through z and $z_{1}$ is perpendicular to the line through $z_{2}$ and $z_{3}$ , then $\arg (z)$ is equal to :

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

$\tan^{- 1} (3) - π$

$\tan^{- 1} (\frac{2}{\sqrt{5}}) - π$

$\tan^{- 1} (\frac{24}{7}) - π$

$\tan^{- 1} (\frac{3}{4}) - π$

answer is B.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Slope of BC = $\frac{3 - 5}{4 - 0} = - \frac{1}{2}$

Slope of AP = 2

equation of AP: $y - 4 = 2 (x - 3) \Rightarrow y = 2 (x - 1)$

P lies on circle $x^{2} + y^{2} = 25$

$\Rightarrow x^{2} + (2 (x - 1))^{2} = 25 \Rightarrow x = - \frac{7}{5} and y = - \frac{24}{5} \Rightarrow \arg (z) = \tan^{- 1} (\frac{24}{7}) - π$

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test