### Home > PC3 > Chapter 4 > Lesson 4.1.2 > Problem4-28

4-28.

In parts (a) and (b) below, calculate the product for each pair of complex numbers whose imaginary parts have opposite signs. Pairs of complex numbers such as these are called complex conjugates. Use any patterns you discover to answer parts (c) through (e).

1. $2+i$, $2-i$

1. $3-5i$, $3+5i$

Your answers to parts (a) and (b) should be strictly real numbers.

1. What complex number can you multiply $3+2i$ by to get a real number?

2. What is the complex conjugate of $a+bi$?

3. What happens when you multiply any complex number by its conjugate?