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Apr 14, 2018 at 23:30 comment added Jens @L.K I posted this answer as a response to the one by Zzz and therefore took over the definition of the angle from that answer. But that angle is actually the (negative of) the direction angle of the branch cut plus $\pi$. A more useful definition that really uses the angle of the branch cut is in the answer I gave here. It also gives the result you expect with the value of the second argument corresponding to the true branch angle.
Apr 14, 2018 at 17:24 comment added L.K. I think @Zzz has right sign. May be you would like to consider it. Let me know if I am wrong, but I checked it(properly hope so). E.g. myLog[Exp[3 I Pi], Pi] = 3 I Pi, however, in your case, it comes out to be -I Pi, which is not even in the cut range(i.e from Pi to 3 Pi). I hope I am not talking bullshit
Nov 18, 2012 at 3:26 history answered Jens CC BY-SA 3.0