1. **State the problem:** Add and subtract the complex numbers \((6 - \sqrt{-16}) + (-16 + \sqrt{-9})\) and \((6 - \sqrt{-16}) - (-16 + \sqrt{-9})\). 2. **Recall the rule for square roots of negative numbers:** For any positive number \(a\), \(\sqrt{-a} = i\sqrt{a}\), where \(i\) is the imaginary unit with \(i^2 = -1\). 3. **Simplify each square root:** \(\sqrt{-16} = 4i\) and \(\sqrt{-9} = 3i\). 4. **Rewrite the expressions:** Add: \((6 - 4i) + (-16 + 3i)\) Subtract: \((6 - 4i) - (-16 + 3i)\) 5. **Perform addition:** Combine real parts: \(6 + (-16) = -10\) Combine imaginary parts: \(-4i + 3i = -i\) Sum = \(-10 - i\) 6. **Perform subtraction:** Distribute the minus sign: \(6 - 4i + 16 - 3i = (6 + 16) + (-4i - 3i)\) Combine real parts: \(22\) Combine imaginary parts: \(-7i\) Difference = \(22 - 7i\) **Final answers:** Sum = \(-10 - i\) Difference = \(22 - 7i\)