Answer
$41$
Work Step by Step
Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the given expression, $
(5+4i)(5-4i)
,$ is equivalent
\begin{align*}
&
(5)^2-(4i)^2
\\&=
25-16i^2
.\end{align*}
Using $i^2=-1$, the expression above is equivalent to
\begin{align*}
&
25-16(-1)
\\&=
25+16
\\&=
41
.\end{align*}
Hence, $(5+4i)(5-4i)$ evaluates to $
41
$.
