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If $x=1+2 i$, then the value of $x^3+7 x^2-x+16$ is
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Verified Answer
The correct answer is:
-17 + 24 i
We have $x-1=2 i \quad \Rightarrow x^2-2 x+5=0$
$$
\begin{aligned}
x^3+7 x^2-x+16 & =x\left(x^2+7 x-1\right)+16 \\
& =x[(0)+9 x-6]+16 \\
& =9 x^2-6 x+16 \\
& =9\left(x^2-2 x+5\right)+12 x-29 \\
& =-17+24 i
\end{aligned}
$$
$$
\begin{aligned}
x^3+7 x^2-x+16 & =x\left(x^2+7 x-1\right)+16 \\
& =x[(0)+9 x-6]+16 \\
& =9 x^2-6 x+16 \\
& =9\left(x^2-2 x+5\right)+12 x-29 \\
& =-17+24 i
\end{aligned}
$$
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