2
$\begingroup$

enter image description here

Log(1) = 0 for both Domains. I have problems to determine log(e). I hope you can help me out here.

EDIT: I have to determine log(e) for both simply connected regions 1) and 2) which you can see in the picture above.

  • 0
    @parsiad These are two simply connected regions with a branch of Log defined on them such that $Log(1) = 0$. – 2017-01-21
  • 0
    Edited the original post. Thanks – 2017-01-21
  • 2
    Connect $1$ to $e$ with a contour through each domain, and integrate $1/z$ along it. Once you have chosen the contour, you can forget the funny-looking domains and replace the contour with an easier one that is homotopic to it within $\mathbb C\setminus\{0\}$ ... – 2017-01-21
  • 0
    @Situ: retracted close vote after edit – 2017-01-21
  • 0
    Do you mean the contour integral of the logarithm? Because the logarithm of $e$ will always be $1$... – 2017-01-21

0 Answers 0