1. **State the problem:** Simplify the complex fraction $$\frac{10}{1+2i}$$ and write the answer in the form $a + bi$. 2. **Formula and rules:** To simplify a complex fraction, multiply numerator and denominator by the conjugate of the denominator. The conjugate of $1+2i$ is $1-2i$. 3. **Multiply numerator and denominator:** $$\frac{10}{1+2i} \times \frac{1-2i}{1-2i} = \frac{10(1-2i)}{(1+2i)(1-2i)}$$ 4. **Calculate denominator using difference of squares:** $$(1+2i)(1-2i) = 1^2 - (2i)^2 = 1 - (-4) = 1 + 4 = 5$$ 5. **Calculate numerator:** $$10(1-2i) = 10 - 20i$$ 6. **Write the fraction:** $$\frac{10 - 20i}{5}$$ 7. **Simplify by dividing both terms by 5:** $$\frac{10}{5} - \frac{20i}{5} = 2 - 4i$$ 8. **Final answer:** The simplified form is $$2 - 4i$$. This matches the option $2 - 4i$.