Question: Simplify the expression to a + bi form:
$(-2 - 9i)(-9 + 4i)$
1. **State the problem:** Simplify the product of two complex numbers $(-2 - 9i)$ and $(-9 + 4i)$ 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:**
$$ (-2 - 9i)(-9 + 4i) = (-2)(-9) + (-2)(4i) + (-9i)(-9) + (-9i)(4i) $$
4. **Calculate each term:**
$$ (-2)(-9) = 18 $$
$$ (-2)(4i) = -8i $$
$$ (-9i)(-9) = 81i $$
$$ (-9i)(4i) = -36i^2 $$
5. **Substitute $i^2 = -1$ and simplify:**
$$ -36i^2 = -36(-1) = 36 $$
6. **Combine like terms:**
$$ 18 + 36 + (-8i + 81i) = 54 + 73i $$
7. **Final answer:**
$$ \boxed{54 + 73i} $$