Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 51

$38+9i$

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $ (6-5i)(3+4i) ,$ simplifies to \begin{array}{l}\require{cancel} 6(3)+6(4i)-5i(3)-5i(4i) \\\\= 18+24i-15i-20i^2 \\\\= 18+9i-20i^2 \\\\= 18+9i-20(-1) \\\\= 18+9i+20 \\\\= 38+9i .\end{array}