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Complex Functions basic concept

  1. Sep 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Describe the domain of definition that is understood for each of the functions:

    (a) [tex]f(z) = \frac{1}{1 - |z|^2}[/tex]

    (b) [tex] f(z) = \frac{z}{z + \bar{z}}[/tex]

    (c) [tex]f(z) = Arg(\frac{1}{z})[/tex]

    (d) [tex]f(z) = \frac{1}{z^2+1}[/tex]

    2. Relevant equations

    A function f defined on S is a rule that assigns to each z in S a complex number w. The number w is called the value of f at z and is denoted by f(z); that is w = f(z). The set S is called the domain of definition of f.

    3. The attempt at a solution
    I really do not know how I should approach the problem. Since it is an odd problem the book has only this listed as answers (b) [tex]Rez \not= 0[/tex] (d) [tex]z \not= \pm i[/tex]

    I understand that for (b) and (d) that these values will make the denominator = 0. What I do not understand is what I should be describing in (a) and (c). Is it really that simple of a question where you just describe only where the functions are undefined? Anyone care give me any suggestions on where to even start thinking? because I am really struggling on this problem that should be easy since it's the first one of the 2nd chapter.
     
  2. jcsd
  3. Sep 17, 2009 #2

    LCKurtz

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    Yes, it is that easy.
     
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