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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