https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ Math lessons that click Sat, 13 Aug 2022 16:54:11 +0000 hourly 1 https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/#comment-395935 Sun, 05 Sep 2021 19:41:54 +0000 http://betterexplained.com/?p=686#comment-395935 […] ex=1+x1!+x22!+x33!+⋯cos(x)=1−x22!+x44!−x66!+⋯sin(x)=x−x33!+x55!−x77!+⋯ 将 ex 中的 x 换成 ±ix ，因为 (±i)2=−1,(±i)3=∓i,(±i)4=1,⋯ ，所以 e+xi=1+ix1!−x22!−ix33!+x44!+⋯=(1+x44!−x66!+⋯)+i(x−x33!+x55!−x77!+⋯)=cos(x)+isin(x)e−xi=cos(x)−isin(x) 如果非要理解 e 的 i 次方是什么意思的话，可以参考： https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ […]

]]> https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/#comment-394807 Tue, 13 Jul 2021 03:03:57 +0000 http://betterexplained.com/?p=686#comment-394807 […] https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ […]

]]> https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/#comment-362623 Tue, 01 Jan 2019 14:55:00 +0000 http://betterexplained.com/?p=686#comment-362623 Hi everybody. I just wanted to let you know that there are great disproves to Euler’s formula. Here you go: https://math.stackexchange.com/questions/2984910/how-is-eulers-formula-wrong
http://mathforum.org/library/drmath/view/51629.html
http://mathforum.org/library/drmath/view/53907.html
http://mathcentral.uregina.ca/QQ/database/QQ.09.11/h/anonymous1.html

]]> https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/#comment-361329 Sun, 23 Dec 2018 20:00:00 +0000 http://betterexplained.com/?p=686#comment-361329 How did Benjamin Pierce handle i if not as rotation? If he could calculate Euler’s formula, he probably knew that it is rotation. But what he probably did not understand, is WHY it is rotation, i.e. what is e doing here, and what is the definition of exponents here. And these questions are still not answered.

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