1. **State the problem:** Divide the complex numbers $(-2 + i)$ by $(1 + 3i)$. 2. **Formula and rule:** To divide complex numbers, multiply numerator and denominator by the conjugate of the denominator. The conjugate of $1 + 3i$ is $1 - 3i$. 3. **Multiply numerator and denominator:** $$\frac{-2 + i}{1 + 3i} \times \frac{1 - 3i}{1 - 3i} = \frac{(-2 + i)(1 - 3i)}{(1 + 3i)(1 - 3i)}$$ 4. **Expand numerator:** $$(-2)(1) + (-2)(-3i) + i(1) + i(-3i) = -2 + 6i + i - 3i^2$$ 5. **Simplify numerator using $i^2 = -1$:** $$-2 + 6i + i - 3(-1) = -2 + 7i + 3 = 1 + 7i$$ 6. **Expand denominator:** $$(1)(1) - (3i)(3i) = 1 - 9i^2$$ 7. **Simplify denominator using $i^2 = -1$:** $$1 - 9(-1) = 1 + 9 = 10$$ 8. **Write the fraction:** $$\frac{1 + 7i}{10}$$ 9. **Express as separate real and imaginary parts:** $$\frac{1}{10} + \frac{7}{10}i$$ **Final answer:** $$\frac{-2 + i}{1 + 3i} = \frac{1}{10} + \frac{7}{10}i$$