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How to tell that 1/(z+2i) is not analytic?

  1. Feb 17, 2012 #1
    hi as shown above, i have come across this expression. But i am not sure how to tell if it is not analytic in the circle |z-2|=4, clockwise.
    expression: 1/(z+2i)

    On top of that, can anyone give me a general idea of how to see if the expression is analytic or not analytic without using the cauchy's equation.

    pls help. thx.
     
  2. jcsd
  3. Feb 17, 2012 #2

    HallsofIvy

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    Well, that circle contains the point -2i at which f(x) does not even exist.
     
  4. Feb 17, 2012 #3
    but how do u tell that f(x) does not exist there?

    does it mean the function will be come infinite when z=-2i and thus telling us it is not analytic at that point?
     
    Last edited: Feb 17, 2012
  5. Feb 17, 2012 #4

    chiro

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    Consider the properties of divergence and also other analytic properties like limits: the limit must be the same from both sides and continuity must hold (among the other properties of analytic functions).
     
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