Question: User: $(4+6i)(9-2i)$
1. **State the problem:** Multiply the complex numbers $4+6i$ and $9-2i$.
2. **Recall the formula:** To multiply two 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:**
$$ (4+6i)(9-2i) = 4 \times 9 + 4 \times (-2i) + 6i \times 9 + 6i \times (-2i) $$
4. **Calculate each term:**
$$ = 36 - 8i + 54i - 12i^2 $$
5. **Simplify $i^2$ term:**
Since $i^2 = -1$,
$$ -12i^2 = -12 \times (-1) = 12 $$
6. **Combine like terms:**
$$ 36 + 12 + (-8i + 54i) = 48 + 46i $$
7. **Final answer:**
$$ (4+6i)(9-2i) = 48 + 46i $$