Question

The value of $x^3+7x^2-x+16$ when $x=1+2i$ is ,

• A. $17-24i$
• B. $-17+24i$
• C. $-17-24i$
• D. $17+24i$

Answer 1

Answer: (B)

We have, $x=1+2i$
$\Rightarrow x-1=2i$
$\Rightarrow x^2-2x+5=0$
Now, $x^3+7x^2-x+16$
$=x\left(x^2-2x+5\right)+9\left(x^2-2x+5\right)+\left(12x-29\right)$
$=x\left(0\right)+9\left(0\right)+12x-29$
$=12\left(1+2i\right)-29$
$=-17+24i$