If $g (x) = x^{4} {- x}^{3} + x^{2} + 3 x - 5$ , find $g (2 + 3 i)$

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Solution

$g (x) = x^{4} - x^{3} + x^{2} + 3 x - 5$
$= x^{2} (x^{2} + 1) - x (x^{2} - 3) - 5$
$x = 2 + 3 i$
$x^{2} = 4 - 3 + 12 i = 1 + 12 i$
$= (1 + 12 i) (2 + 12 i) - (1 + 12 i) (- 2 + 12 i) - 5$
$= 2 + 12 i + 24 i - 144 + 2 + 24 i - 12 i + 144 - 5$
$= - 1 + 48 i$ .

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