The value of z for which |z+i| = |z-i| are
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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

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Best answer

SOLUTION —

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).

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