If $x = 3 + i$ then $x^{3} - 3 x^{2} - 8 x + 15 =$

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-18

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-15

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Solution

The correct option is C -15
$x = 3 + i \Rightarrow x - 3 = i \Rightarrow (x - 3)^{2} = - 1$
$\Rightarrow x^{2} - 6 x + 10 = 0$
$∴ x^{3} - 3 x^{2} - 8 x + 15$
$= x (x^{2} - 6 x + 10) + 3 (x^{2} - 6 x + 10) - 15$
$= x (0) + 3 (0) - 15 = - 15.$

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