Answer
The standard form of the expression $\left( 8-4i \right)\left( -3+9i \right)$ is $12+84i$.
Work Step by Step
Consider the expression $\left( 8-4i \right)\left( -3+9i \right)$.
Use the FOIL method.
$\left( 8-4i \right)\left( -3+9i \right)=-24+72i+12i-36{{i}^{2}}$
Replace the value ${{i}^{2}}=-1$.
$\left( 8-4i \right)\left( -3+9i \right)=-24+72i+12i-36\left( -1 \right)$
Make a group of real and imaginary terms.
$\left( 8-4i \right)\left( -3+9i \right)=-24+36+72i+12i$
Simplify the real and imaginary terms.
$\begin{align}
& \left( 8-4i \right)\left( -3+9i \right)=\left( -24+36 \right)+\left( 72+12 \right)i \\
& =12+84i
\end{align}$
Therefore, the standard form of the expression $\left( 8-4i \right)\left( -3+9i \right)$ is $12+84i$.
