Answer
$73$
Work Step by Step
Using $(a+b)(a-b)=a^2-b^2$, or the product of the sum and difference of like terms, and using the properties of radicals, the given expression, $
(3+8i)(3-8i)
,$ simplifies to
\begin{array}{l}\require{cancel}
(3)^2-(8i)^2
\\\\=
9-64i^2
\\\\=
9-64(-1)
\\\\=
9+64
\\\\=
73
.\end{array}