1. **State the problem:** Write each expression in the form $a + bi$, where $a$ and $b$ are real numbers. 2. **Recall the rules:** - To subtract complex numbers, subtract their real parts and their imaginary parts separately. - To multiply complex numbers, use the distributive property (FOIL) and remember that $i^2 = -1$. --- ### A) $(3 - 4i) - (-2 + 9i)$ 3. Apply subtraction: $$ (3 - 4i) - (-2 + 9i) = 3 - 4i + 2 - 9i $$ 4. Combine like terms: $$ (3 + 2) + (-4i - 9i) = 5 - 13i $$ --- ### B) $(3 - 4i) - (-2 + 9i)$ (same as A) 5. This is the same as part A, so the answer is: $$ 5 - 13i $$ --- ### C) $(3 - 4i)(-2 + 9i)$ 6. Use FOIL: $$ 3 \times (-2) + 3 \times 9i - 4i \times (-2) - 4i \times 9i $$ 7. Calculate each term: $$ -6 + 27i + 8i - 36i^2 $$ 8. Combine like terms: $$ -6 + (27i + 8i) - 36i^2 = -6 + 35i - 36i^2 $$ 9. Substitute $i^2 = -1$: $$ -6 + 35i - 36(-1) = -6 + 35i + 36 $$ 10. Simplify: $$ (-6 + 36) + 35i = 30 + 35i $$ --- **Final answers:** - A) $5 - 13i$ - B) $5 - 13i$ - C) $30 + 35i$