### Home > PC3 > Chapter 11 > Lesson 11.1.4 > Problem11-76

11-76.

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

1. $(3 + 2i)(3 − 2i)$

$3(3) − 3(2i) + 3(2i) − 4i^2$

1. $(\sqrt { 5 }− i\sqrt { 3 })(\sqrt { 5 }+ i\sqrt { 3 })$

$(\sqrt{5})(\sqrt{5})+(\sqrt{5})(\textit{i}\sqrt{3})-(\textit{i}\sqrt{3})(\sqrt{5})-(\textit{i}\sqrt{3})(\textit{i}\sqrt{3})$

1. What does $\sqrt { 3 }+ 7i$ need to be multiplied by so that the result is a whole number?

The answers for parts (a) and (b) are both whole numbers. How are the factors being multiplied the same or different?

2. What does $a + bi$ need to be multiplied by so that the result is a real number?