Euler's identity is actually eix=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 eiπ is obviously -1.--Nigel Galloway (talk) 14:31, 9 August 2021 (UTC)
- FWIW, the Wikipedia article on the subject describes eix=cos(x)+i.sin(x) as Euler's formula and agrees with the task author that eiπ + 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)
- For what it is worth, the "also known as" and stupid white spacing was not added by me, (the original task author). I doubt if Gerard Schildberger ever bothers to go back and look at what a mess all that ridiculous indentation and white space makes with a mobile browser. I suppose he belongs to the school of "It looks good on my screen so it must be right. Tough luck for you." Sigh. --Thundergnat (talk) 21:03, 10 August 2021 (UTC)
- I do go back and look, regardless of what Thundergnat thinks and/or doubts. I do not see the mess that Thundergnat is claiming that he sees. I do not have a "mobile browser", so I can't verify what Thundergnat is claiming to see is a mess and his claims of ridiculous indentations and white space. I assume that he could use the same browser that I use on a PC and see that I am seeing. I can only view the output for the browsers that I have access to and those browser output(s) that I can verify. It is possible that he belongs to the school that if it looks bad on his screen, it must look bad on my screen. Double sigh. Discourse would be more friendly if less pejorative wording and/or phraseology would be used. Of what I have observed in the past is what normally follows is a doubling-down and even more unfriendly discussions. -- Gerard Schildberger (talk) 03:21, 11 August 2021 (UTC)
- There is more information at the Wolfram MathWorld™ entry: Euler formula where it states on the 1st sentence:
The Euler formula, sometimes also called the Euler identity ...
- You can also do a search on Wolfram MathWorld™ (using the Search MathWorld feature) for Euler identity that also has a pointer to the same entry. -- Gerard Schildberger (talk) 03:47, 11 August 2021 (UTC)