## College Algebra (10th Edition)

$10-5i$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $(3-4i)(2+i) ,$ use the FOIL Method and the equivalence $i^2=-1.$ $\bf{\text{Solution Details:}}$ 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} 3(2)+3(i)-4i(2)-4i(i) \\\\= 6+3i-8i-4i^2 \\\\= 6-5i-4i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 6-5i-4(-1) \\\\= 6-5i+4 \\\\= 10-5i .\end{array}