Never liked that form of the Euler's formula. I prefer the following:

    (-1)ˣ = cos(πx) + i sin(πx)

▲ penteract 2 hours ago | parent | next [-]

My 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.

▲ badlibrarian 5 hours ago | parent | prev [-]

That's not the point of the Identity. You exponentiated the beauty right out of it.

	▲	xeonmc 4 hours ago \| parent [-]
		Beauty 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?"