Euler's Identity - Maple Help
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Euler's Identity

Main Concept

Euler's identity is the famous equality where:

 • e is Euler's number ≈ 2.718
 • i is the imaginary number;

This is a special case of Euler's formula: , where :

Visually, this identity can be defined as the limit of the function as n approaches infinity. More generally,  can be defined as the limit of   as $n$ approaches infinity.

For a given value of z, the plot below shows the value of  as n increases to infinity, as well as the sequence of line segments from  to . Each additional line segment represents an additional multiplication by . For  , it can be seen that the point approaches $\mathit{-}\mathit{1}$.

Click Play/Stop to start or stop the animation or use the slider to adjust the frames manually. Choose a different value of z to see how the plot is affected. Use the controls to adjust the view of the plot.

 z =



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