Chapter 9 - Trigonometric Identities, Models, and Complex Numbers - 9.6 Complex Numbers and De Moivre's Theorem - Exercises and Problems for Section 9.6 - Exercises and Problems - Page 392: 9

$-3-4i$.

$\text{Solution:}$ Step 1: $(2+3i)+(-5-7i)=2+3i-5-7i $ Step 2: Adding two complex numbers is done by adding real and imaginary parts separately $$(2+3i)+(-5-7i)=(2-5)+(3i-7i)$$ Factoring out $i$, $$(2+3i)+(-5-7i)=(2-5)+(3-7)i $$ Simplify $$(2+3i)+(-5-7i)=(-3)+(-4)i=-3-4i$$ Step 3: The Cartesian form of $(2+3i)+(-5-7i)$ is $-3-4i$.