Categories
 Oscillations and Waves Applets
 Acoustics Applets
 Signal Processing Applets
 Electricity and Magnetism Applets
 Electrodynamics Applets
 Quantum Mechanics Applets
 Quantum Phisics Applets
 Linear Algebra Applets
 Vector Calculus Applets
 Thermodynamics Applets
 Miscellaneous Applets
 Electronics for Beginners
 Videos on Youtube
 Components Datasheet
 Links
Euler's Formula Applet

This applet is a graphical demonstration of Euler's formula: e^{ix} = cos x + i sin xWe can generalize this to complex numbers: e^{z} = e^{x} (cos y + i sin y)where z = x + i y. In the applet, z is shown as a green dot on the complex plane. e^{z} is shown as a red dot. The unit circle is shown in gray. z goes from π to π and back again, which causes e^{z} to go around the unit circle. 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 z (the light blue line from 1 to 1+z), and then z^{2}/2, and so on. You can select another value of e^{z} by clicking anywhere with the mouse. If you want to select another value of z with the mouse, change the popup menu from "Mouse = Select exp(z)" to "Mouse = Select z". 