Let $z$ be a complex number of constant modulus such that $z^{2}$ is purely imaginary then the number of possible values of z is

2

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1

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4

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infinite

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Solution

The correct option is B $4$
Let $z = x + i y$
$z^{2}$ is purely imaginary
$z^{2} = x^{2} - y^{2} + 2 x y i$
$x = \pm y$
so 4 pair can possible for constant modulus.
$(x, y), (- x, - y), (x, - y), (- x, y)$

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