Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 57

$50$

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, $ (-7+i)(-7-i) ,$ simplifies to \begin{array}{l}\require{cancel} (-7)^2-(i)^2 \\\\= 49-i^2 \\\\= 49-(-1) \\\\= 49+1 \\\\= 50 .\end{array}