Question

The value of $z$ for which

$|z+i|=|z-i|$ are

(A) Any real number

(B) Any complex number

(C) Any natural number

(D) None of these

Answer 1

Let $z=x+i y,|x+i y+i|=|x+i y-i|$

$\Rightarrow  \sqrt{x^2+(1+y)^2}=\sqrt{x^2+(y-1)^2} $

$\Rightarrow  y^2+2 y+1=y^2-2 y+1 \Rightarrow y=0 $

$\therefore  z=x$

So, The correct option will be (A).