4 ms·
Never liked that form of the Euler's formula. I prefer the following: (-1)ˣ = cos(πx) + i sin(πx)
by xeonmc 11mo ago
Never liked that form of the Euler's formula. I prefer the following:
(-1)ˣ = cos(πx) + i sin(πx)
- badlibrarian 11mo agoThat's not the point of the Identity. You exponentiated the beauty right out of it.
- xeonmc 11mo agoBeauty is in the eye of the beholder. Instead shoehorning it into an arbitrary symbol salad by gimping its generality, I prefer the one which makes a statement: "What does it mean to apply inversion partially?"
- penteract 11mo agoMy objection to that is that there isn't a particularly natural reason not to say (-1)ˣ = cos(πx) - i sin(πx) As a formula about e^iπx, there is no such conflict.