## College Algebra (10th Edition)

$-12-9i$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $3i(-3+4i) ,$ use the Distributive Property and the equivalence $i^2=-1.$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 3i(-3)+3i(4i) \\\\= -9i+12i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} -9i+12(-1) \\\\= -9i-12 \\\\= -12-9i .\end{array}