Talk:Euler's identity

Euler's identity is actually e^ix=cos(x)+i.sin(x). The example given is a special case when when x=π. cos π is -1 and sin π is 0. Thus e^iπ is obviously -1.--Nigel Galloway (talk) 14:31, 9 August 2021 (UTC)

FWIW, the Wikipedia article on the subject describes e^ix=cos(x)+i.sin(x) as Euler's formula and agrees with the task author that e^iπ + 1 = 0 is called Euler's identity. I have no idea whether this is correct terminology or not. --PureFox (talk) 14:48, 9 August 2021 (UTC)

Somewhat inconsistently used AKA's. However, if we adopt "formula" for the general case, and "identity" for the special case, and the task here is regarding the special case (which must necessarily pre-assume the validity of the general case), then as per Nigel the "proof" is trivial - boils down to "proving" that -1 + 1 = 0 (to the limit of IEEE 754 for the "-1" in most non-symbolic languages), right? --Davbol (talk) 16:10, 9 August 2021 (UTC)

That, of course, is true but the point at issue is whether the terminology is correct or not. I don't think Thundergnat will want to change it from Euler's identity without seeing some authoritative proof that it's the wrong term. --PureFox (talk) 16:48, 9 August 2021 (UTC)