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Understanding Euler's Formula | BetterExplained

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Published on Jul 17, 2010

Companion video to the article at http://betterexplained.com/articles/i.... Key analogies:

* Multiplication as a transformation
* Exponential growth as a continuous change
* Imaginary numbers as rotation
* Exponential, imaginary growth as continuous rotation
* Radians as distance traveled around the circle

Combining the analogies, you can see e^ix as a rotation around the circle, equivalent to cos(x) + i*sin(x), which is the position in a "grid system".

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