Complex numbers are used extensively in electronics to analyze and understand alternating signals like those used in radio and television. While the concept of using real and imaginary numbers seems strange, complex numbers actually make it easier to work with alternating signals by simplifying calculations. Complex numbers are needed because some equations that describe alternating signals have no real number solutions, requiring the use of imaginary numbers to fully represent solutions.

1. Complex Numbers
(Not that hard)
5.9

2. An Equation with “No Solutions”?

3. Real World Uses of Complex Numbers
Complex numbers are used a great deal in
electronics. The main reason for this is they make
the whole topic of analyzing and understanding
alternating signals much easier. This seems odd at
first, as the concept of using a mix of real and
'imaginary' numbers to explain things in the real
world seem crazy! Once you get used to
them, however, they do make a lot of things clearer.
The problem is understanding what they 'mean'
and how to use them in the first place.
http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/signals/complex/cmplx.html

4. Imaginary Unit

5. Simplifying Square Roots of Negative
Numbers

6. Simplifying with Pure Imaginary
Numbers

8. Solving Equations with Imaginary
Solutions

9. Complex Number System
Understanding the Relationship between
Number Types
Real Numbers
b=0
Pure
Imaginary
Numbers
a=0

10. Equal Complex Numbers

11. Equating Complex Numbers

12. Adding and Subtracting Complex
Numbers

13. Multiply Complex Numbers

14. Divide Complex Numbers

15. Assignment
• P. 274;42-62 all