#### Answer

$-27+12i$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
3i(4+9i)
,$ use the Distributive Property. Then use $i^2=-1$.
$\bf{\text{Solution Details:}}$
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(4)+3i(9i)
\\\\=
12i+27i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
12i+27(-1)
\\\\=
12i-27
\\\\=
-27+12i
.\end{array}