Re:The exponential function is a miracle
by thaumasiotes on Friday September 13, 2019 @03:42AM
(#20960016)
> I think e^i pi = -1 is drastically overrated. That is typically the definition of exponentiating to a complex power, that e^ix = sin x + i cos x.
Yes, but it's the definition of exponentiating to a complex power because it is easily proven by reference to the real Taylor series of those functions. The complex definition is motivated by the real result, not -- as you imply -- the other way around.
(Also, you have it backwards; e^ix is cos x + i sin x.)
Yes, but it's the definition of exponentiating to a complex power because it is easily proven by reference to the real Taylor series of those functions. The complex definition is motivated by the real result, not -- as you imply -- the other way around.
(Also, you have it backwards; e^ix is cos x + i sin x.)