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