Answer
The standard form of the expression $\left( -5+4i \right)\left( 3+i \right)$ is $-19+7i$.
Work Step by Step
Consider the expression $\left( -5+4i \right)\left( 3+i \right)$.
Use the FOIL method.
$\left( -5+4i \right)\left( 3+i \right)=-15-5i+12i+4{{i}^{2}}$
Replace the value ${{i}^{2}}=-1$.
$\left( -5+4i \right)\left( 3+i \right)=-15-5i+12i+4\left( -1 \right)$
Make a group of real and imaginary terms.
$\left( -5+4i \right)\left( 3+i \right)=-15-4+12i-5i$
Simplify the real and imaginary terms.
$\begin{align}
& \left( -5+4i \right)\left( 3+i \right)=\left( -15-4 \right)+\left( 12-5 \right)i \\
& =-19+7i
\end{align}$
Therefore, the standard form of the expression $\left( -5+4i \right)\left( 3+i \right)$ is $-19+7i$.
