#### Answer

$12-16i$

#### Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, the given expression, $
(4-2i)^2
,$ simplifies to
\begin{array}{l}\require{cancel}
(4)^2+2(4)(-2i)+(-2i)^2
\\\\=
16-16i+4i^2
\\\\=
16-16i+4(-1)
\\\\=
16-16i-4
\\\\=
12-16i
.\end{array}