Question

The number of complex numbers $z$ such that $|z-1|=|z+1|=|z-i|$, is

• A. 0
• B. 1
• C. 2
• D. $\infty$

Answer 1

Answer: (A)

$|z-1|-|z+1|-|z-i|$
Point which is equidistant from $A,B$ and $C$ is $(0,0)$.
$\therefore z=0$ is only complex number which satisfies the given relation.