关于复变函数中对数函数的一点讨论

Brief Discussion on the Logarithm Function of the Complex Function

在复变函数课本中关于初等函数这一节中的对数函数部分,课本中提到Lnzn=nLnz,Lnz1/n=1/nLnz两个式子一般是不成立的,本文将针对上述两个式子是否成立展开讨论,证明了Lnzn=nlnz在复数域上一般不成立,而Lnz1/n=1/nLnz在复数域上是成立的.

In the part of logarithmic function in the textbooks of complex function, it is mentioned that the two formulas Lnzn=nLnz and Lnn√z=1/nLnz can not be established. This article will have a discussion on these two formulas, and prove that Lnz^n≠nLnz is usually not right, but Lnn√z=1/nLnz is right in complex number field.