#### Answer

$-3-4i$

#### Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, the given expression, $
(1-2i)^2
,$ simplifies to
\begin{array}{l}\require{cancel}
(1)^2+2(1)(-2i)+(-2i)^2
\\\\=
1-4i+4i^2
\\\\=
1-4i+4(-1)
\\\\=
1-4i-4
\\\\=
-3-4i
.\end{array}