1. **State the problem:** Add the complex numbers $(3 - 5i)$ and $(7 - 2i)$. 2. **Formula:** To add complex numbers, add their real parts and their imaginary parts separately: $$ (a + bi) + (c + di) = (a + c) + (b + d)i $$ 3. **Apply the formula:** Real parts: $3 + 7 = 10$ Imaginary parts: $-5 + (-2) = -7$ 4. **Write the result:** $$ 10 - 7i $$ 5. **Explanation:** When adding complex numbers, treat the real and imaginary parts like separate numbers. Add the real parts together and the imaginary parts together to get the final sum. --- 1. **State the problem:** Subtract the complex number $(3 + 5i)$ from $(4 - 8i)$. 2. **Formula:** To subtract complex numbers, subtract their real parts and their imaginary parts separately: $$ (a + bi) - (c + di) = (a - c) + (b - d)i $$ 3. **Apply the formula:** Real parts: $4 - 3 = 1$ Imaginary parts: $-8 - 5 = -13$ 4. **Write the result:** $$ 1 - 13i $$ 5. **Explanation:** Subtraction works similarly to addition, but you subtract the corresponding parts instead.