Mathematics - Complex Number Question with Solution | TestHub

Let $z=x+iy$ $$\begin{array}{lll}|z-1|=|z+1|& \Rightarrow \mathrm{Re}z=0& \Rightarrow x=0\\ |z-1|=|z-i|& \Rightarrow x=y& \\ |z+1|=|z-i|& \Rightarrow y=-x& \end{array}$$ Only $(0,0)$ will satisfy all conditions. $\Rightarrow$ Number of complex number $z=1$