Q. The locus of the point $z = x + y - iy$ satisfying the equation $\left| \frac{z - 1}{z + 1} \right| = 1$ is given by
A) $x = 0$
B) $y = 0$
C) $x = y$
D) $x + y = 0$
Explanation
(a)
Since, $\left| \frac{x + iy - 1}{x + iy + 1} \right| = 1$
$\Rightarrow \ \ \ \ \ \sqrt{(x - 1)^{2} + y^{2}} = \sqrt{(x + 1)^{2} + y^{2}}$
$\Rightarrow \ \ \ \ \ \ \ x^{2} - 2x + 1 + y^{2} = x^{2} + 1 + 2x + y^{2}$
$\Rightarrow \ \ \ \ x = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.