Q. The locus represented by the equation $|z - 1| = |z - i|$ is
A) A circle of radius 1
B) An ellipse with foci at 1 and $–i$
C) A line through the origin
D) A circle on the line joining 1 and $–i$ as diameter
Explanation
(c)
Given, $|z - 1| = |z - i|$
$\Rightarrow \ \ \ z$ lies on the perpendicular bisector of the line joining (1, 0)
And (0, 1) and it is a straight line passing through origin.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.