Answer
$9+58i$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the given expression, $
(8+i)(2+7i)
,$ is equivalent to
\begin{align*}
&
8(2)+8(7i)+i(2)+i(7i)
\\&=
16+56i+2i+7i^2
\\&=
16+56i+2i+7(-1)
&\text{ (use $i^2=-1$)}
\\&=
16+56i+2i-7
.\end{align*}
Combining the real parts and the imaginary parts, the expression above is equivalent to
\begin{align*}
&
(16-7)+(56i+2i)
\\&=
9+58i
.\end{align*}
Hence, the simplified form of the given expression is $
9+58i
$.
