37Dividing complex numbers

Write $\displaystyle \dfrac{7 + i}{1 - i}$ in the form $\displaystyle a + bi$.

The answer is 3 + 4i. Multiply top and bottom by the conjugate 1 + i, so the bottom becomes 1² − i² = 2 and the top becomes 7 + 8i + i² = 6 + 8i, then divide by 2. Check: (3+4i)(1−i) = 7 + i ✓.