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Wyrd Smythe's avatar

I understand Gauss wanted to call the "imaginary" axis the "lateral" axis, which would have been a lot less confusing for math students. There is also the nice fact that understanding multiplication as rotation explains something else that students can find confusing: It makes sense that multiplying positive (real) numbers results in a positive real number, and it sort of makes sense that multiplying a positive real number times a negative real number gives a negative number, but much harder to understand why multiplying two negative numbers results in a positive number. But it's just a matter of 180° rotations.

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skybrian's avatar

If you want a more visual explanation of Euler’s formula, I wrote one a long while back:

https://docs.google.com/presentation/d/1oMNjkDp-LieSGnZEwNpceG8KTIvbnus9olu3KqnM5bg/

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