Answer
$5+14i$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $
(4+i)(2+3i)
,$ simplifies to
\begin{array}{l}\require{cancel}
4(2)+4(3i)+i(2)+i(3i)
\\\\=
8+12i+2i+3i^2
\\\\=
8+14i+3i^2
\\\\=
8+14i+3(-1)
\\\\=
8+14i-3
\\\\=
5+14i
.\end{array}