1. Using the Quadratic Formula to Find Complex Roots (Including Complex Conjugates)

2. Complex Number
A number consisting of a real and imaginary part. Usually written in the following form (where a and b are real numbers):
Example: Solve 0 = 2x2 – 2x + 10
a = b = c = 1 -2 10

3. Classifying the Roots of a Quadratic
Describe the amount of roots and what number set they belong to for each graph:
1 Repeated Real Root because it has one x-intercept (bounces off)
2 Real Roots because it has two x-intercepts
2 Complex Roots because it has no x-intercepts
A Quadratic ALWAYS has two roots

4. Determining whether the Roots are Real or Complex
What part of the Quadratic Formula determines whether there will be real or complex solutions?
Discriminant < 0

5. The sum and product of complex conjugates are always real numbers
For any complex number:
The Complex Conjugate is:
The sum and product of complex conjugates are always real numbers
Example: Find the sum and product of 2 – 3i and its complex conjugate.

6. Complex Roots Are Complex Conjugates
A quadratic equation y = ax2 + bx + c in which b2 – 4ac < 0 has two roots that are complex conjugates.
Example: Find the zeros of y = 2x2 + 6x + 10
and
Complex Conjugates!