Answer
The standard form of the expression $\left( 7-i \right)\left( 2+3i \right)$ is $17+19i$.
Work Step by Step
Consider the expression,
$\left( 7-i \right)\left( 2+3i \right)$
Apply the FOIL method on the above expression
Therefore,
$\begin{align}
& \left( 7-i \right)\left( 2+3i \right)=7\left( 2 \right)+7\left( 3i \right)-i\left( 2 \right)-i\left( 3i \right) \\
& =14+21i-2i-3{{i}^{2}}
\end{align}$
As ${{i}^{2}}=-1$
So,
$14+21i-2i-3{{i}^{2}}=14+21i-2i+3$
Combine the real part and imaginary part separately and either add or subtract as required.
Therefore,
$\begin{align}
& 14+21i-2i+3=\left( 14+3 \right)+\left( 21i-2i \right) \\
& =17+\left( 21-2 \right)i \\
& =17+19i
\end{align}$
Thus,
$\left( 7-i \right)\left( 2+3i \right)=17+19i$
Hence, the standard form of the expression $\left( 7-i \right)\left( 2+3i \right)$ is $17+19i$.
