Express the following expression in the form $\;\normalsize a + \normalsize ib : \large\frac{(\normalsize 3 + \normalsize i \sqrt{5})(\normalsize 3 - \normalsize i \sqrt{5})}{(\normalsize \sqrt{3} + \normalsize i \sqrt{2})-(\normalsize \sqrt{3} - \normalsize i \sqrt{2})}$

Question

$(a)\;-\large\frac{5\sqrt{2}}{2} \normalsize i\qquad(b)\;-\large\frac{7\sqrt{2}}{2} \normalsize i\qquad(c)\;-\large\frac{9\sqrt{2}}{2} \normalsize i\qquad(d)\;-\large\frac{3\sqrt{2}}{2} \normalsize i$