Answer
$10-5i$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(3-4i)(2+i)
,$ use the FOIL Method and the equivalence $i^2=-1.$
$\bf{\text{Solution Details:}}$
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel}
3(2)+3(i)-4i(2)-4i(i)
\\\\=
6+3i-8i-4i^2
\\\\=
6-5i-4i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
6-5i-4(-1)
\\\\=
6-5i+4
\\\\=
10-5i
.\end{array}
