Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 62

$5+12i$

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, the given expression, $ (3+2i)^2 ,$ simplifies to \begin{array}{l}\require{cancel} (3)^2+2(3)(2i)+(2i)^2 \\\\= 9+12i+4i^2 \\\\= 9+12i+4(-1) \\\\= 9+12i-4 \\\\= 5+12i .\end{array}