1. **State the problem:** Simplify the expression $ (6 + 4i) + (-3 + i) $ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. **Recall the rule:** When adding complex numbers, add the real parts together and the imaginary parts together. 3. **Add the real parts:** $6 + (-3) = 3$ 4. **Add the imaginary parts:** $4i + i = 5i$ 5. **Combine the results:** The simplified expression is $3 + 5i$. **Final answer:** $3 + 5i$