Answer
$23+i$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(7-2i)(3+i)
,$ use the FOIL method. Then use $i^2=-1$ and combine like terms.
$\bf{\text{Solution Details:}}$
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}
7(3)+7(i)-2i(3)-2i(i)
\\\\=
21+7i-6i-2i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
21+7i-6i-2(-1)
\\\\=
21+7i-6i+2
.\end{array}
Combining like terms results to
\begin{array}{l}\require{cancel}
(21+2)+(7i-6i)
\\\\=
23+i
.\end{array}
