Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 54

$8+31i$

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}