Question

If $2x=3+5i$, then the value of $2x^3+2x^2-7x+72$ is

• A. $4$
• B. $-4$
• C. $8$
• D. $-8$

Answer 1

The correct option is A $4$

$2x=3+5\overrightarrow{i}$

$\therefore x=\frac{3+5\overrightarrow{i}}{2}$

$\therefore x^3=\frac{27+135\overrightarrow{i}-225-125\overrightarrow{i}}{8}$

$\therefore x^3\frac{-198+10\overrightarrow{i}}{8}$

$\therefore x^2=\frac{9-25+30\overrightarrow{i}}{4}$

$\therefore x^2=\frac{30\overrightarrow{i}-16}{4}$

$\therefore 2x^3+2x^2-7x+72=2\left(\frac{-198+10\overrightarrow{i}}{8}\right)+2\left(\frac{30\overrightarrow{i}-16}{4}\right)-7\left(\frac{3+5\overrightarrow{i}}{2}\right)+72$

$=(\frac{-99}{2}-8-\frac{21}{2}+72)+\left[(\frac{10}{4}+15)\frac{-35}{2}\right]\overrightarrow{i}$

$=\left(\frac{-99-16-21+144}{2}\right)+\left(\frac{10+60-70}{4}\right)\overrightarrow{i}$

$=\frac{-136+144}{2}=\frac{8}{2}$