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Math Help - ln z - continuous, holomorphic(analytic)

  1. #1
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    ln z - continuous, holomorphic(analytic)

    Showing that ln z is analytic in Re \leq 0 I used CR-equations. I guess that's sufficient since a function needs to be analytic to satisfy C-R equations.
    I'm also supposed to show that ln z is discontinuous in Re < 0 Briefly: I showed that -\pi,  \pi hits the same point if the radius is the same.

    Now to my question, not a part of the exercise, but I like to know. How can I show that ln z is continuous in for instance Re > 0 I have another thread about continuous functions, but that's a more general prof. I like to put get together an example with some help from you folks.
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  2. #2
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    It turns out I misunderstood the exercise somewhat. I had to show that ln z is analytic in the whole complex plane, but the negative real part. This expression got the better of me. \Omega = \mathbb{C} \  \{z | z \in \mathbb{R}, z \leq 0 \}
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