Question: Simplify the expression to a + bi form:
$(5 - 2i)(9 + 10i)$
1. **State the problem:** Simplify the product of two complex numbers $(5 - 2i)$ and $(9 + 10i)$ into the form $a + bi$.
2. **Recall the formula:** When multiplying complex numbers $(a + bi)(c + di)$, use the distributive property:
$$ (a + bi)(c + di) = ac + adi + bci + bdi^2 $$
Remember that $i^2 = -1$.
3. **Apply the formula:**
$$ (5 - 2i)(9 + 10i) = 5 \times 9 + 5 \times 10i - 2i \times 9 - 2i \times 10i $$
4. **Calculate each term:**
$$ = 45 + 50i - 18i - 20i^2 $$
5. **Simplify the imaginary unit term:**
Since $i^2 = -1$,
$$ -20i^2 = -20 \times (-1) = 20 $$
6. **Combine like terms:**
$$ 45 + 20 + (50i - 18i) = 65 + 32i $$
7. **Final answer:**
The expression simplifies to
$$ \boxed{65 + 32i} $$