Find 'x' and 'y' if $x^{2} - y^{2} - i (2 x + y) = 2 i$

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Solution

$x^{2} - y^{2} - i (2 x + y) = 2 i$
$2 x + y = - 2, x^{2} - y^{2} = 0$
$x^{2} = y^{2}$
$x = \pm y$
$x = y, 3 x = - 2, x = - 2 / 3 = y$
$x = - y, - x = - 2, y = 2$

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