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Analytic Function

  1. Sep 29, 2008 #1
    Hi, I have some questions regarding how to find the analytisity region of a funtion.
    I'm a little confuse after I studied the definition of analytic function: which it saids
    [if a function f is differentiable at every z in A, then f is analytic on A]

    eg. Log z is analytic on the entire complex plane EXCEPT the -ve real axis.
    Which make sense to me since Log z is undefind when x<=0 & y=0 , for z=x+iy

    Log z^2 is analytic on the entire complex plane again EXCEPT z=0, and exclude the
    Imaginary axis. Is that right?

    I'm wondering if there's a way to actually compute/calculate the region instead of doing it in the head?
    Since Log z & Log z^2 is kinda basic, it'll be hard to do if it is comething like Log (1+2/z)

    Thanks in advance

  2. jcsd
  3. Sep 29, 2008 #2


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    log(-1) CAN be defined since e^(i*pi)=-1. The upper case 'L' in Log is not is not just ornamental. It's a branch of log that's undefined for negative reals precisely so it can be uniquely defined for all other complex numbers. You can't compute why a function like that is undefined. Where it's undefined is a matter of convention. Look up "analytic continuation".
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