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

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

Complex Numbers and Quadratic Equations

Solution:

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

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