CPM Homework Help : PC3 Problem 11-76

Compute each of the following products of complex numbers. Recall that $i^{2} = −1$ .

$(\sqrt { 5 }− i\sqrt { 3 })(\sqrt { 5 }+ i\sqrt { 3 })$
Step (b):
$(\sqrt{5})(\sqrt{5})+(\sqrt{5})(\textit{i}\sqrt{3})-(\textit{i}\sqrt{3})(\sqrt{5})-(\textit{i}\sqrt{3})(\textit{i}\sqrt{3})$

What does $\sqrt { 3 }+ 7i$ need to be multiplied by so that the result is a whole number?
Hint (c):
The answers for parts (a) and (b) are both whole numbers. How are the factors being multiplied the same or different?
What does $a + bi$ need to be multiplied by so that the result is a real number?