1. **State the problem:** Simplify the expression $7 \div (3 - i)$. 2. **Formula and rules:** To divide by a complex number, multiply numerator and denominator by the conjugate of the denominator. The conjugate of $3 - i$ is $3 + i$. 3. **Multiply numerator and denominator by the conjugate:** $$\frac{7}{3 - i} \times \frac{3 + i}{3 + i} = \frac{7(3 + i)}{(3 - i)(3 + i)}$$ 4. **Calculate the denominator using difference of squares:** $$(3 - i)(3 + i) = 3^2 - i^2 = 9 - (-1) = 9 + 1 = 10$$ 5. **Expand the numerator:** $$7(3 + i) = 21 + 7i$$ 6. **Write the fraction:** $$\frac{21 + 7i}{10}$$ 7. **Simplify by dividing both terms by 10:** $$\frac{21}{10} + \frac{7}{10}i$$ **Final answer:** $$\frac{21}{10} + \frac{7}{10}i$$