Answer
$19+17i$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method and using $i^2=-1$, the given expression $
(5-i)(3+4i)
,$ simplifies to
\begin{array}{l}\require{cancel}
5(3)+5(4i)-i(3)-i(4i)
\\\\=
15+20i-3i-4i^2
\\\\=
15+20i-3i-4(-1)
\\\\=
15+20i-3i+4
\\\\=
(15+4)+(20i-3i)
\\\\=
19+17i
.\end{array}
