Euler's Formula Applet Demonstrates Taylor series expansion of complex exponentials
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Euler's Formula Applet Description

Euler's Formula Applet a graphical demonstration of Euler's formula: eix = cos x + i sin x We can generalize this to complex numbers: ez = ex (cos y + i sin y) where z = x + i y. In the applet, z is shown as a green dot on the complex plane. ez is shown as a red dot. The unit circle is shown in gray. z goes from -π to π and back again, which causes ez to go around the unit circle. ez 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 z2/2, and so on. You can select another value of ez 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". Take Euler's Formula Applet for atets run to fully asses its capabilities!

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