1. **State the problem:** Multiply the complex numbers $ (9-2i) $ and $ (1+3i) $. 2. **Formula used:** To multiply two complex numbers $ (a+bi) $ and $ (c+di) $, use the distributive property: $$ (a+bi)(c+di) = ac + adi + bci + bdi^2 $$ Remember that $ i^2 = -1 $. 3. **Apply the formula:** $$ (9-2i)(1+3i) = 9 \times 1 + 9 \times 3i - 2i \times 1 - 2i \times 3i $$ 4. **Calculate each term:** $$ = 9 + 27i - 2i - 6i^2 $$ 5. **Simplify $ i^2 $ term:** $$ = 9 + 27i - 2i - 6(-1) $$ 6. **Simplify further:** $$ = 9 + 27i - 2i + 6 $$ 7. **Combine like terms:** $$ = (9 + 6) + (27i - 2i) $$ $$ = 15 + 25i $$ **Final answer:** $$ 15 + 25i $$