Q. If the amplitude of $z - 2 - 3i$ is $\frac{\pi}{4}$, then the locus of $z = x + iy$, is
A) $x + y - 1 = 0$
B) $x - y - 1 = 0$
C) $x + y + 1 = 0$
D) $x - y + 1 = 0$
Explanation
(d)
We have, $z - 2 - 3i = x + iy - 2 - 3i = (x - 2) + i(y - 3)$
Given, $\tan^{- 1}\left( \frac{y - 3}{x - 2} \right) = \frac{\pi}{4}$
$\Rightarrow \ \ \ \ y - 3 = x - 2$
$\Rightarrow \ \ \ \ x - y + 1 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.