Question

Locus of the point z satisfying the equation $|z-1|+|z-i|=\sqrt{2}$ is

• A. Circle
• B. A straight line
• C. Point
• D. Complex $x-y$ plane

Answer 1

The correct option is B A straight line

Given $|z-1|+|z-i|=\sqrt{2}$

Also, we know that if

$|z-z_1|+|z-z_2|=2k$ represents a straight line when $|z_1-z_2|=2k$.

In given equation $|z_1-z_2|=|1-i|=\sqrt{2}=2k$.

So, above equation represents a straight line.