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Exponential Functions and Euler's Formula
- nh23423fefe 1y agoi actually thought the opposite. i found it extremely illuminating to see exp(ix) partition the power series into even and odd terms and collect into cos and sine. i just always thought of the chain of functions that are their own derivatives. f = f' => f = exp f = f'' => f = cosh or sinh f = f'''' = -f'' => f = cos or sine if you dont skip cosh/sinh the pattern makes more sense. and obviously f = f'''' strongly suggests 1 = i^4