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Math Help - Complex Limit Question (Log)

  1. #1
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    Complex Limit Question (Log)

    Hey guys,

    I'm having trouble trying to PROVE why the lim z-->0 of Log(z) = infinity

    What I've done (doesnt look right, obviously, else I wouldnt post!) is the following:-

    Log(z) = ln|z| + iArg(z)

    |z| = 0
    arg(0) = 0

    Log(z) = ln(0)

    But. My arguement now is that as z-->0, ln|z| will APPROACH negative infinity, but (recalling a priniciple mentioned in class) the complex plane only has "infinity" not plus/minus inf, so that goes to "infinity"

    As I said, this looks like a terrible argument. Can someone please clarify/assst with the proof plz?

    Thanks in advanced,

    XPhaTe
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  2. #2
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    As an aside, I'm also struggling with lim(z-->-1)

    My initial feeling was non-existance, but now Im not sure
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  3. #3
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    Quote Originally Posted by exphate View Post
    As an aside, I'm also struggling with lim(z-->-1)

    My initial feeling was non-existance, but now Im not sure
    Where is your branch cut?

    Quote Originally Posted by exphate View Post
    Hey guys,

    I'm having trouble trying to PROVE why the lim z-->0 of Log(z) = infinity

    What I've done (doesnt look right, obviously, else I wouldnt post!) is the following:-

    Log(z) = ln|z| + iArg(z)

    |z| = 0
    arg(0) = 0

    Log(z) = ln(0)

    But. My arguement now is that as z-->0, ln|z| will APPROACH negative infinity, but (recalling a priniciple mentioned in class) the complex plane only has "infinity" not plus/minus inf, so that goes to "infinity"

    As I said, this looks like a terrible argument. Can someone please clarify/assst with the proof plz?

    Thanks in advanced,

    XPhaTe
    Note that z = 0 is a branch point.
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