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Math Help - Domain

  1. #1
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    Domain

    For each function describe the domain:

    f(z)=Arg(1/z)

    f(z)=1/(1-lzl^2)

    Thanks
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  3. #3
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by bethh View Post
    For each function describe the domain:

    f(z)=Arg(1/z)

    f(z)=1/(1-lzl^2)

    Thanks
    The domain will be the entirety of \mathbb{C} except the few points that cause a singularity (i.e. where the denominator will be 0).

    For the first one, the domain excludes only z=0.

    For the second one the domain excludes all points of the form \cos(\theta) +i\sin(\theta), in other words, the unit circle |z|=1.
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