## Intermediate Algebra (12th Edition)

$23+i$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $(7-2i)(3+i) ,$ use the FOIL method. Then use $i^2=-1$ and combine like terms. $\bf{\text{Solution Details:}}$ Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel} 7(3)+7(i)-2i(3)-2i(i) \\\\= 21+7i-6i-2i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 21+7i-6i-2(-1) \\\\= 21+7i-6i+2 .\end{array} Combining like terms results to \begin{array}{l}\require{cancel} (21+2)+(7i-6i) \\\\= 23+i .\end{array}