Perform the indicated operations \& simplify. Add: \( (-7+\sqrt{-64})+(23-\sqrt{-25}) \) sum \( =\square \) Subtract: \( (-7+\sqrt{-64})-(23-\sqrt{-25}) \) difference \( =\square \)

Let's simplify the given expressions step by step. ### 1. Addition: \[ (-7 + \sqrt{-64}) + (23 - \sqrt{-25}) \] First, simplify the square roots of negative numbers using \( i = \sqrt{-1} \): \[ \sqrt{-64} = 8i \quad \text{and} \quad \sqrt{-25} = 5i \] Now, substitute these back into the expression: \[ (-7 + 8i) + (23 - 5i) \] Combine like terms: \[ (-7 + 23) + (8i - 5i) = 16 + 3i \] **Sum**: \[ \boxed{16 + 3i} \] ### 2. Subtraction: \[ (-7 + \sqrt{-64}) - (23 - \sqrt{-25}) \] Again, simplify the square roots: \[ \sqrt{-64} = 8i \quad \text{and} \quad \sqrt{-25} = 5i \] Substitute these into the expression: \[ (-7 + 8i) - (23 - 5i) \] Distribute the negative sign and combine like terms: \[ -7 + 8i - 23 + 5i = (-7 - 23) + (8i + 5i) = -30 + 13i \] **Difference**: \[ \boxed{-30 + 13i} \]