Answer
$-12-9i$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
