1. **Problem Statement:** Verify the expression $$\frac{z_1 + z_2}{z_1 - z_2}$$ where $$z_1 = 3 + 4i$$ and $$z_2 = -3 - 4i$$. 2. **Recall:** Complex numbers are of the form $$a + bi$$ where $$i^2 = -1$$. 3. **Calculate numerator:** $$z_1 + z_2 = (3 + 4i) + (-3 - 4i) = 0 + 0i = 0$$ 4. **Calculate denominator:** $$z_1 - z_2 = (3 + 4i) - (-3 - 4i) = 3 + 4i + 3 + 4i = 6 + 8i$$ 5. **Form the fraction:** $$\frac{z_1 + z_2}{z_1 - z_2} = \frac{0}{6 + 8i} = 0$$ 6. **Conclusion:** The value of the expression is $$0$$. This verifies the given expression.