Find the real numbers $x$ and $y$ , if $(x - i y) (1 + i)$ is the conjugate of $- 3 - 2 i$

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Solution

$(x - i y) (1 + i) = - 3 + 2 i$

$x + x i - y i + y = - 3 + 2 i$

$x + y = - 3$ ....(i)
$x - y = 2$ ....(ii)

Adding (i) and (ii),
$x + y = - 3$
$+$
$x - y = 2$
____________
$2 x = - 1$

$x = \frac{- 1}{2}$

Putting the value of $x$ in (i), we get,

$y = \frac{- 5}{2}$

$∴ x = \frac{- 1}{2} a n d y = \frac{- 5}{2}$

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