If $x = 2 + 3 i$ , then the value of $x^{4} - x^{3} + 10 x^{2} + 3 x - 5$ is

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Solution

$x = 2 + 3 i \Rightarrow x^{2} - 4 x + 13 = 0$
$∴$ $x^{4} - x^{3} + 10 x^{2} + 3 x - 5$
$= (x^{2} - 4 x + 13) (x^{2} + 3 x + 9) + 122 = 122$

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