Answer
$21-25i$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the given expression, $
(1-9i)(3+2i)
,$ is equivalent to
\begin{align*}
&
1(3)+1(2i)-9i(3)-9i(2i)
\\&=
3+2i-27i-18i^2
\\&=
3+2i-27i-18(-1)
&\text{ (use $i^2=-1$)}
\\&=
3+2i-27i+18
\\&=
(3+18)+(2i-27i)
&\text{ (combine like terms)}
\\&=
21+(-25i)
\\&=
21-25i
.\end{align*}
Hence, the given expression simplifies to $
21-25i
$.