Question: Simplify the expression to a + bi form:
$$(8 - 3i)(4 + 4i)$$
1. **State the problem:** Simplify the expression $$(8 - 3i)(4 + 4i)$$ into the form $a + bi$ where $a$ and $b$ are real numbers.
2. **Recall the formula:** To multiply two complex numbers, use the distributive property (FOIL):
$$ (a + bi)(c + di) = ac + adi + bci + bdi^2 $$
Remember that $$i^2 = -1$$.
3. **Apply the formula:**
$$ (8 - 3i)(4 + 4i) = 8 \times 4 + 8 \times 4i - 3i \times 4 - 3i \times 4i $$
4. **Calculate each term:**
$$ = 32 + 32i - 12i - 12i^2 $$
5. **Simplify the imaginary terms:**
$$ 32i - 12i = 20i $$
6. **Replace $$i^2$$ with $$-1$$:**
$$ -12i^2 = -12 \times (-1) = 12 $$
7. **Combine real parts:**
$$ 32 + 12 = 44 $$
8. **Write the final expression:**
$$ 44 + 20i $$
**Final answer:**
$$ \boxed{44 + 20i} $$