Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 64

$21+20i$

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, the given expression, $ (-5-2i)^2 ,$ simplifies to \begin{array}{l}\require{cancel} (-5)^2+2(-5)(-2i)+(-2i)^2 \\\\= 25+20i+4i^2 \\\\= 25+20i+4(-1) \\\\= 25+20i-4 \\\\= 21+20i .\end{array}