Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 55

$73$

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}