Answer
$6-10i$
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 $
(-8+2i)(-1+i)
,$ simplifies to
\begin{array}{l}\require{cancel}
-8(-1)-8(i)+2i(-1)+2i(i)
\\\\=
8-8i-2i+2i^2
\\\\=
8-8i-2i+2(-1)
\\\\=
8-8i-2i-2
\\\\=
(8-2)+(-8i-2i)
\\\\=
6-10i
.\end{array}