If $x=1+2 i$, then the value of $x^3+7 x^2-x+16$ is

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Aicharya · Accepted Answer

We have $x-1=2 i \quad \Rightarrow x^2-2 x+5=0$ $\begin{aligned} x^3+7 x^2-x+16 & =x\left(x^2+7 x-1ight)+16 \ & =x[(0)+9 x-6]+16 \ & =9 x^2-6 x+16 \ & =9\left(x^2-2 x+5ight)+12 x-29 \ & =-17+24 i \end{aligned}$

If $x=1+2 i$, then the value of $x^3+7 x^2-x+16$ is

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