HINT: TRY PUSHING F11 KEY TO GET BIGGER SCREEN IF THE FLASH PROGRAM IS TOO BIG FOR SCREEN. (Put curser up in toolbar and click region before hitting F11)

Before you can understand the Fourier series as a sum of complex exponentials, you need to first understand complex exponentials. The four flash programs below will help you visualize complex numbers and e^jwt.

This assumes you know about complex numbers as roots of algebraic formulas such as : x^2+1, but that you want insight into e^jwt, and how sine and cosine waves are made from e^jwt and e^-jwt.

Demonstrates how e^jx creates a complex number	Click here
Adds time to allow you to look at e^jwt. Lets you think about how e^jwt converts one complex number into another one, and gets you familiar with the circular motion of phasors	Click here
Allows you to add two phasors together and see how a real sinusoidal wave is generated with two opposite rotating phasors.	Click here
Add four frequencies together as represents by eight rotating phasors. Explore how a time shift results in different amounts of phase shifts at each frequency.	Click here