引言在这篇短文里,我們向讀者介紹一种新的建立尤拉公式的方法。我們不用一般数学分析里所用的方法,而用一个人家熟知的重要极限来建立尤拉公式。同时,我們考虑到尤拉公式的应用很广泛,也很重要,因此,順便列举了一些应用。其中特别請大家注意应用4和5,显然这样做是不够严格的,但我們想借此向讀者說明:当在复数城里研究初等函数时会出現实数城里沒有的有趣性质,从而帮助我們更深地理解初等实函数。这对中学数学教师是有帮助的。§1.尤拉公式e~(θi)=cosθ+isinθ的推导在数学分析里已經証明了一个重要极限 e~θ=(?)(1+θ/n)~n,这里θ为任意实数。推广这个結果于θi,得 e~(θi)=(?)(1+θi/n)~n (1)这里θ为任意实数,而i为虚数单位。現在我們来計 Introduction In this short essay, we introduce the reader to a new method of establishing Euler’s formula. Instead of using the methods used in general mathematical analysis, we use the important limits that people are familiar with to build the Euler formula. At the same time, we consider that the application of Euler’s formula is very extensive and important. Therefore, some applications are listed by the way. In particular, please pay attention to applications 4 and 5. Obviously this is not strict enough, but we would like to take this to explain to readers that when studying elementary functions in plural cities, there will be interesting properties that are not found in real cities, which will help us deeper. Understand the elementary real function. This is helpful for middle school math teachers. § 1. Derivation of Euler’s formula e~(θi)=cosθ+isinθ In mathematical analysis, an important limit e~θ=(?)(1+θ/n)~n has been proved, where θ is an arbitrary real number. To generalize this result to θi, get e~(θi)=(?)(1+θi/n)~n (1) where θ is an arbitrary real number and i is an imaginary unit. Now let’s count