Find the value of $x^{3} - x^{2} + x + 46$ if $x = 2 + 3 i$

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Solution

Given that,

$x = 2 + 3 i$

$x^{2} = (2 + 3 i) = 4 + 9 i + 12 i$

$x^{2} = - 5 + 12 i$

$x^{3} = - 10 + 24 i - 15 i + 36 i^{2}$

$x^{3} = - 46 + 9 i$

$x^{3} - x^{2} + x + 46$

$\Rightarrow - 46 + 9 i + 5 - 12 i + 2 + 3 i + 46$

$\Rightarrow 7$

$x^{3} - x^{2} + x + 46 = 7$

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