Question

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

• A. $-11+24i$
• B. $-17+24i$
• C. $-17-24i$
• D. $-1+24i$

Answer 1

The correct option is B $-17+24i$

Given function $f\left(x\right)=x^3+7x^2-x+16$

We know that $(a+b{)}^3=a^2+3ab(a+b)+b^3(a+b{)}^2=a^2+b^2+2ab$

When $x=1+2$

$f(1+2i)=(1+2i{)}^2+(1+2i{)}^2-(1+2i)+16=1+8i^3+3\times 2i\times (1+2i)+7\times (1+4i+4i^2)-(1+2i)+16=1+8i^3+6i+12i^2+7+28i+28i^2-1-2i+16=1-8i+6i-12+7+28i-28-1-2+16[\because i^3=-i,i^2=-1]=-17+24i$