1. ALGEBRA TWO
CHAPTER FIVE
QUADRATIC FUNCTIONS
5.4 Complex Numbers

2. LEARNING GOALS
Solve Quadratic Equations with Complex Solutions and perform operations with Complex Numbers.
Apply Complex Numbers to Fractal Geometry.

3. What is the solution of?:

4. Imaginary Unit
Until now, you have always been told that you can’t take the square root of a negative number. If you use imaginary units, you can!
The imaginary unit is i.
i =
It is used to write the square root of a negative number.

5. Property of the square root of negative numbers
If r is a positive real number, then
Examples:

6. *For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead.
Example:

7. Examples

8. Complex Numbers A complex number has a real part & an imaginary part.
Standard form is:
Real part
Imaginary part
Example: i

9. The Complex plane
Real Axis
Imaginary Axis

10. Graphing in the complex plane

11. Adding and Subtracting (add or subtract the real parts, then add or subtract the imaginary parts)
Ex:
Ex:
Ex:

12. Multiplying Treat the i ’s like variables, then change any that are not to the first power
Ex:
Ex:

13. Dividing Complex Numbers 1) multiply the numerator and denominator by the complex conjugate of the denominator (conjugate: change sign between the terms ex: conjugate of x-1 is x+1)

14. Dividing Complex Numbers

16. Absolute Value of a Complex Number
The distance the complex number is from the origin on the complex plane.
If you have a complex number
the absolute value can be found using:

17. Examples
Which of these 2 complex numbers is closest to the origin?
-2 + 5i

18. ASSIGNMENT
WRITE pg
#19, 21, 29, 31, 39, 41, 49, 51, 57, 59, & 65