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Comment by dls2016 | Hacker News Reader

dls2016

> introduced imaginary numbers as rotations initially

How would you do this without developing the exponential first?

Well any complex number a + bi can be described as a transformation matrix

    |a -b|
    |b  a|

So you could start by just asking what it means to transform the plane

Ok but in a college algebra class it’s very easy to ask “what is the inverse of the squaring operation?” Not so clear a path to the action of a matrix on the plane.

I have successfully discussed this in an advanced calculus class.

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