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

0

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1

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2

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Infinite

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Solution

The correct option is C $1$

$| z - i | = | z - 1 | = | z + 1 |$
$L e t z = x + i y$
$| x + i (y - 1) | = | (x - 1) + i y | = | (x + 1) + i y |$
$m e a n s p o i n t (x, y) i s e q u i d i s t a n t f r o m (1, 0), (- 1, 0) a n d (0, 1)$
$a n d i n t h i s c a s e o n l y a p o i n t (0, 0)$
$e x i s t w h i c h w i l l b e e q u i d i s t a n t f r o m t h e s e p o i n t s .$
$h e n c e o n l y 1 s u c h c o m p l e x$ $n u m b e r e x i s t s$

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