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Complex Numbers

Find the valu...

Question

Find the value of $x^{3} + 7 x^{2} - x + 16$ , where $x = 1 + 2 i$

- 17 + 24 i

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24 + 17 i

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17 - 24 i

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24 - 17 i

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Solution

The correct option is A $- 17 + 24 i$
$x^{2} = (1 + 2 i)^{2} = 1 + 4 i^{2} + 4 i = 4 i - 3$
$x^{3} = x \times x^{2} = (1 + 2 i) (4 i - 3) = 4 i + 8 i^{2} - 3 - 6 i = - 2 i - 11$
$x^{3} + 7 x^{2} - x + 16 = 24 i - 17$
$- 17 + 24 i$

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