This applet is a graphical demonstration of Euler's formula:

We can generalize this to complex numbers:e= cos^{ix}x+isinx

wheree=^{z}e(cos^{x}y+isiny)

*e ^{z}* can be evaluated using a power series; the terms
of this series are shown in alternating shades of blue, starting with
1 (the blue line from the origin to 1), and then

You can select another value of *e ^{z}* by clicking
anywhere with the mouse. If you want to select another value of

Huge thanks to Bob Hanson and his team for help converting this applet to javascript.