Question

The locus represented by $|z-1|=|z+i|$ 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 join of 1 and $-i$ as diameter

Answer 1

Answer: (C)

We have,
$\Rightarrow |(x-1)+i y|=|x+i(y+1)| $
$\Rightarrow (x-1)^{2}+y^{2}=x^{2}+(y+1)^{2}$
$\Rightarrow x+y=0$,
which is a line through the origin.