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  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 .

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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