Answer
$-33-56i$
Work Step by Step
Using $i^2=-1$ and $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression $
(4-7i)^2
$ is equivalent to
\begin{array}{l}
(4)^2+2(4)(-7i)+(-7i)^2
\\=
16-56i+49i^2
\\=
16-56i+49(-1)
\\=
-33-56i
.\end{array}
