1. We start with part (a): Find the sum $ (2 + 5i) + (4 - i) $. 2. Add the real parts: $2 + 4 = 6$. 3. Add the imaginary parts: $5i + (-i) = 4i$. 4. So, the result for part (a) is $6 + 4i$. 5. Next, part (b): Find $ (\sqrt{16} - 3i) - (-3 + \sqrt{-36}) $. 6. Simplify $\sqrt{16} = 4$. 7. Recognize that $\sqrt{-36} = \sqrt{36} \times \sqrt{-1} = 6i$. 8. Substitute these back: $ (4 - 3i) - (-3 + 6i) $. 9. Distribute the minus: $4 - 3i + 3 - 6i$. 10. Combine the real parts: $4 + 3 = 7$. 11. Combine the imaginary parts: $-3i - 6i = -9i$. 12. So, the result for part (b) is $7 - 9i$. Final answers: - (a) $6 + 4i$ - (b) $7 - 9i$