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Complex Log?

  1. Sep 9, 2008 #1

    tgt

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    Would it be okay to redefine the complex definition of Log and define it for example C\[0,infinity)?

    I guess then you would have Log z = log |z| + i Arg(z)

    where -Pi<=Arg(z)<Pi

    Everything would work fine?

    But then you can't have Log 5 for example which would be very counter unintuitive.
     
  2. jcsd
  3. Sep 10, 2008 #2

    Gib Z

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    Why can't you have Log 5? I see no problems with that. You can redefine anything you want - how useful it ends up being in its applications is another question though.
     
  4. Sep 10, 2008 #3

    tgt

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    To have a Log function defined on the complex plane, you need a branch cut somewhere. Exactly where is arbitary right? So what happens if you choose the positive real line? You'd lose Log (r) for r in the positive reals, including Log(5).
     
  5. Sep 10, 2008 #4

    Gib Z

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  6. Sep 10, 2008 #5

    tgt

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    It should be assuming log(|x|) is the logarithm of the reals. I'm just saying since the branch cut can be applied anywhere, what happens if we apply it on the real line? Then we don't have Log(5). Then that wouldn't be a good definition would it?
     
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