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The problem with that is that complex numbers initially emerge as roots of polynomials with real coefficients. Getting to affine transformations from there seem
by jameshart 10y ago
The problem with that is that complex numbers initially emerge as roots of polynomials with real coefficients. Getting to affine transformations from there seems a much bigger leap than asserting there is a square root of -1.
- E6300 10y agoThe video linked in this post will only make sense if you accept that x e^(theta i) and x k are respectively the rotation part and the scaling part of a linear transformation of x. I'm not aware of any other way to intuitively grasp an expression like e^(pi i).
- ouid 10y agothis is an old comment, but e^z (over C) can be defined as the analytic continuation of e^x (over R). This is a much more interesting definition, since it depends on the fact that that function is unique.