If $z$ is a complex number such that $z = {(x + i y)}^{2}$ then find $¯ ¯ ¯ z$ .

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Solution

$z = (x + i y)^{2}$
$\Rightarrow z = x^{2} - y^{2} + 2 i x y$
$\Rightarrow ¯ ¯ ¯ z = x^{2} - y^{2} - 2 i x y$

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