Question

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

Answer 1

Answer: (C)

Given, $|z-1|=|z-i|$
$\Rightarrow$ z lies on the perpendicular bisector of the line joining $(1,0)$ and $(0,1)$ and is a straight line passing through origin.