Never liked that form of the Euler's formula. I prefer the following:
(-1)ˣ = cos(πx) + i sin(πx)
My objection to that is that there isn't a particularly natural reason not to say
(-1)ˣ = cos(πx) - i sin(πx)
That's not the point of the Identity. You exponentiated the beauty right out of it.
My objection to that is that there isn't a particularly natural reason not to say
As a formula about e^iπx, there is no such conflict.