Robert Lacoste's The Darker Side

Appendix B Complex Numbers 101

In this book I used complex numbers from time to time, particularly when discussing impedance matching. Complex numbers are a very powerful and common mathematical representation, but you may not be used to them. Here is a small introduction.

Geometrical Interpretation

Let’s suppose that you have two numbers, a and b, but you want to manage them as a single entity for convenience. You can consider a and b as the coordinates of a point Z on a 2D plane. This is called the “complex plane,” but it is actually a very simple construction: Just measure a distance a on the horizontal axis (called the “real axis” in complex arithmetic) and a distance b on the vertical axis (the “imaginary axis”), and you have located point ...