Answer
The standard form of the expression $\left( 7-5i \right)\left( -2-3i \right)$ is $-29-11i$.
Work Step by Step
Consider the expression $\left( 7-5i \right)\left( -2-3i \right)$.
Use the FOIL method.
$\left( 7-5i \right)\left( -2-3i \right)=-14-21i+10i+15{{i}^{2}}$
Replace the value ${{i}^{2}}=-1$.
$\left( 7-5i \right)\left( -2-3i \right)=-14-21i+10i+15\left( -1 \right)$
Make a group of real and imaginary terms.
\[\left( 7-5i \right)\left( -2-3i \right)=-14-15+10i-21i\]
Simplify the real and imaginary terms.
\[\begin{align}
& \left( 7-5i \right)\left( -2-3i \right)=\left( -14-15 \right)+\left( 10-21 \right)i \\
& =-29-11i
\end{align}\]
Therefore, the standard form of the expression $\left( 7-5i \right)\left( -2-3i \right)$ is $-29-11i$.
