Answer
$14+8i$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the given expression, $
(4+6i)(2-i)
,$ is equivalent to
\begin{align*}
&
4(2)+4(-i)+6i(2)+6i(-i)
\\&=
8-4i+12i-6i^2
\\&=
8-4i+12i-6(-1)
&(\text{use }i^2=-1)
\\&=
8-4i+12i+6
\\&=
(8+6)+(-4i+12i)
&(\text{combine real, imaginary numbers})
\\&=
14+8i
.\end{align*}
Hence, the expression $(4+6i)(2-i)$ simplifies to $14+8i$.
