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Complex analysis continuity of functions

  1. Jan 26, 2009 #1
    1. The problem statement, all variables and given/known data

    The functions Re(z)/|z|, z/|z|, Re(z^2)/|z|^2, and zRe(z)/|z| are all defined for z!=0 (z is not equal to 0)
    Which of them can be defined at the point z=0 in such a way that the extended functions are continuous at z=0???

    It gives the answer to be:
    Only f(z)=zRe(z)/|z|, f(0)=0

    I see that f(0)=0 in this case, but I don't see how this is proven or shown. I don't see why the last equation works and the first three don't.

    3. The attempt at a solution

    I'm completely unsure of how to do this, I would have something if I even knew where to start. Maybe I'm confused about what extended functions are?

    A link to the book:
  2. jcsd
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