Answer
The standard form of the expression $\left( 7+8i \right)\left( 7-8i \right)$ is $113$.
Work Step by Step
Consider the expression,
$\left( 7+8i \right)\left( 7-8i \right)$
The product of the complex number $\left( a+bi \right)$ and its complex conjugate $\left( a-bi \right)$ results in a real number -- that is, $\left( a+bi \right)\left( a-bi \right)={{a}^{2}}+{{b}^{2}}$.
Here, a is 7 and $b$is 8.
$\begin{align}
& \left( 7+8i \right)\left( 7-8i \right)={{7}^{2}}+{{8}^{2}} \\
& =49+64 \\
& =113
\end{align}$
Hence, the standard form of the expression $\left( 7+8i \right)\left( 7-8i \right)$ is $113$.
