Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 58

$41$

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, $ (-4+5i)(-4-5i) ,$ simplifies to \begin{array}{l}\require{cancel} (-4)^2-(5i)^2 \\\\= 16-25i^2 \\\\= 16-25(-1) \\\\= 16+25 \\\\= 41 .\end{array}