#### Answer

$8+31i$

#### Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $
(-4+5i)(3-4i)
,$ simplifies to
\begin{array}{l}\require{cancel}
-4(3)-4(-4i)+5i(3)+5i(-4i)
\\\\=
-12+16i+15i-20i^2
\\\\=
-12+31i-20i^2
\\\\=
-12+31i-20(-1)
\\\\=
-12+31i+20
\\\\=
8+31i
.\end{array}