Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 46

$-6+14i$

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $ 2i(7+3i) ,$ simplifies to \begin{array}{l}\require{cancel} 2i(7)+2i(3i) \\\\= 14i+6i^2 \\\\= 14i+6(-1) \\\\= 14i-6 \\\\= -6+14i .\end{array}