No one ever answered original ZZZ's question in a straightforward shortest code

" Mathematica chooses the branch cut for log(z) to lie along the negative real axis. It it possible to change this so that it lies along the positive axis or elsewhere in the complex plane?"

I don't understand the complicated answers given and the codes don't work. The natural cut should be a jump of imaginary part from -2pi to 0 when crossing the real x axis. Please give short understandable code and verify this

  • $\begingroup$ No that original never answered its question in its original simplest form. A general answer was attempted; I don't understand the code and Mathematica refused it to me $\endgroup$
    – simon
    Dec 30, 2022 at 16:28
  • 1
    $\begingroup$ What is the simplest form? Why don't you post it as an answer? (I can't imagine a simpler form than one of the answers given there.) $\endgroup$
    – Michael E2
    Dec 30, 2022 at 17:54
  • $\begingroup$ I.e. if you want the branch cut at θ = t0, then Log[-Exp[-I t0] z] - I Pi + I t0. $\endgroup$
    – Michael E2
    Dec 30, 2022 at 18:02
  • $\begingroup$ So branch cut at θ = 0, then Log[-Exp[-I *0] z] - I Pi + I *0=Log[-z]-IPi. Won't that jump from -2Pi to 0 crossing +x axis $\endgroup$
    – simon
    Dec 30, 2022 at 20:58
  • $\begingroup$ Yes, it does. Isn't that what you want? $\endgroup$
    – Michael E2
    Dec 30, 2022 at 22:27


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