Chapter 1 - Review Exercises - Page 163: 25

$146$

Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms and using $i^2=-1$, the given expression $ (5-11i)(5+11i) ,$ simplifies to \begin{array}{l}\require{cancel} (5)^2-(11i)^2 \\\\= 25-121i^2 \\\\= 25-121(-1) \\\\= 25+121 \\\\= 146 .\end{array}