## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

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