JEE Main 2022 (Online) 29th June Evening ShiftQuestion 1
Let $\arg(z)$ represent the principal argument of the complex number $z$. Then, $|z|=3$ and $\arg(z-1)-\arg(z+1)=\frac{\pi}{4}$ intersect
Complex Numbers
Solution
$\arg(z-1)-\arg(z+1)=\frac\pi4$ is the angle subtended at $z$ by the segment $[-1,1]$: the upper major arc of the circle with centre $(0,1)$, radius $\sqrt2$. The largest $|z|$ on it is $1+\sqrt2\approx2.414<3$, so it never meets $|z|=3$. Option (C).