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 first simplify the expressions under the square roots. For \(\sqrt{-64}\), we know \( \sqrt{-64} = \sqrt{64} \cdot i = 8i\). For \(\sqrt{-25}\), we have \( \sqrt{-25} = \sqrt{25} \cdot i = 5i\). Now we can rewrite the expression: \((-7 + 8i) + (23 - 5i)\). ### Addition: Combine the real parts and the imaginary parts: \[ (-7 + 23) + (8i - 5i) = 16 + 3i. \] So, the sum is \(16 + 3i\). ### Subtraction: Now for the subtraction: \((-7 + 8i) - (23 - 5i)\). Distributing the negative sign gives: \[ -7 + 8i - 23 + 5i = (-7 - 23) + (8i + 5i) = -30 + 13i. \] So, the difference is \(-30 + 13i\). To summarize: sum \( = 16 + 3i\) difference \( = -30 + 13i\)