Question Detail

(\frac{5+10i}{3+i} \cdot \frac{3-i}{3-i} = \frac{(5+10i)(3-i)}{9+1} = \frac{15 -5i +30i -10i^2}{10} = \frac{15 +25i +10}{10} = \frac{25+25i}{10} = \frac{5}{2} + \frac{5}{2}i). Option C is (\frac{5}{2} + \frac{7}{2}i), which is close but not matching. Option A is (\frac{5}{2} + \frac{9}{2}i). Neither matches exactly. Possibly the numerator was different.