Complex Conjugates Theorem (Jump to: Lecture | Video )

Imagine a and b are real numbers, and that b is not equal to 0. If a + bi is the zero of a polynomial equation, a – bi is also a zero.

Create a polynomial equation that has zeros of 4 and 3 – i.

Remember that conjugates always come in pairs, so our three zeros are 4, (3 - i), and (3 + i).

Figure 1.

Now, we simply multiply our three zeros to find our polynomial equation:

Figure 2.