Question: Find the difference of the following expression: $$(3+i)-(4-5i)$$
1. **State the problem:** We need to find the difference between two complex numbers $$(3+i)$$ and $$(4-5i)$$.
2. **Recall the rule for subtracting complex numbers:** To subtract, subtract the real parts and the imaginary parts separately.
3. **Write the expression:** $$(3+i)-(4-5i) = 3 + i - 4 + 5i$$
4. **Group real and imaginary parts:** $$(3 - 4) + (i + 5i)$$
5. **Simplify each part:** $$-1 + 6i$$
6. **Final answer:** The difference is $$-1 + 6i$$, which corresponds to option b.)