Answer
$10-5i$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(4+3i)(1-2i)
,$ 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}
4(1)+4(-2i)+3i(1)+3i(-2i)
\\\\=
4-8i+3i-6i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
4-8i+3i-6(-1)
\\\\=
4-8i+3i+6
.\end{array}
Combining like terms results to
\begin{array}{l}\require{cancel}
(4+6)+(-8i+3i)
\\\\=
10-5i
.\end{array}
