Answer
$9-23i$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the given expression, $
(-6-5i)(1+3i)
,$ is equivalent to
\begin{align*}
&
-6(1)-6(3i)-5i(1)-5i(3i)
\\&=
-6-18i-5i-15i^2
\\&=
-6-18i-5i-15(-1)
&\text{ (use $i^2=-1$)}
\\&=
-6-18i-5i+15
.\end{align*}
Combining the real parts and the imaginary parts, the expression above is equivalent to
\begin{align*}
&
(-6+15)+(-18i-5i)
\\&=
9+(-23i)
\\&=
9-23i
.\end{align*}
Hence, the simplified form of the given expression is $
9-23i
$.