## Intermediate Algebra (12th Edition)

$153$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $(12+3i)(12-3i) ,$ use the special product on multiplying the sum and difference of like terms. Then use $i^2=-1.$ $\bf{\text{Solution Details:}}$ Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the expression above is equivalent \begin{array}{l}\require{cancel} (12)^2-(3i)^2 \\\\= 144-9i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 144-9(-1) \\\\= 144+9 \\\\= 153 .\end{array}