Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 63

$-5-12i$

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