Answer
The standard form of the expression $\left( 6-7i \right)\left( 2+5i \right)$ is $47+16i$.
Work Step by Step
Consider the expression, $\left( 6-7i \right)\left( 2+5i \right)$
First multiply the first term of each bracket, then the outer terms of both brackets, then the inner terms of both the brackets and finally the inner term of the first bracket with the outer term of the second bracket.
Use the FOIL method.
$\begin{align}
& \left( 6-7i \right)\left( 2+5i \right)=6\left( 2 \right)+6\left( 5i \right)-7i\left( 2 \right)-7i\left( 5i \right) \\
& =12+30i-14i-35{{i}^{2}}
\end{align}$
Use the property, ${{i}^{2}}=-1$.
$\begin{align}
& \left( 6-7i \right)\left( 2+5i \right)=12+30i-14i-35\left( -1 \right) \\
& =12+30i-14i+35
\end{align}$
Combine the real part and the imaginary part.
$\begin{align}
& \left( 6-7i \right)\left( 2+5i \right)=\left( 12+35 \right)+\left( 30i-14i \right) \\
& =47+16i
\end{align}$
Therefore, the standard form of the expression $\left( 6-7i \right)\left( 2+5i \right)$ is $47+16i$.
