Answer
$13-6i$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the given expression, $
(2+i)(4-5i)
,$ is equivalent to
\begin{align*}
&
2(4)+2(-5i)+i(4)+i(-5i)
\\&=
8-10i+4i-5i^2
\\&=
8-10i+4i-5(-1)
&\text{ (use $i^2=-1$)}
\\&=
8-10i+4i+5
.\end{align*}
Combining the real parts and the imaginary parts, the expression above is equivalent to
\begin{align*}
&
(8+5)+(-10i+4i)
\\&=
13+(-6i)
\\&=
13-6i
.\end{align*}
Hence, the simplified form of the given expression is $
13-6i
$.
