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Math Help - Limits of Function with complex numbers

  1. #1
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    Limits of Function with complex numbers

    I am studying for an exam and came across this excercise...
    Let f: D\rightarrow C
    (complex numbers). Suppose a is a limit point of D. If f(x)\rightarrow b as x\rightarrow a, then Re(f(x))\rightarrow Re(b) as x\rightarrow a.

    So we have that if 0<|x-a|<\delta \Longrightarrow |f(x)-b|<\epsilon,
    then, 0<|x-a|<\delta \Longrightarrow |Re(f(x)-Re(b)|<\epsilon.
    However, I'm not sure how to use this to find the apropriate values for epsilon and delta that makes this true. Any help would be appreciated.
    Last edited by zebra2147; October 17th 2010 at 07:18 PM. Reason: format
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  2. #2
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    You have post some serious problems.
    http://www.mathhelpforum.com/math-he...ial-19060.html
    So Why not learn to post in symbols? You can use LaTeX tags.
    You are more likely to receive serious attention if your posting are easy to read.
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  3. #3
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    I am studying for an exam and came across this excercise...
    Let f: D\rightarrow C
    (complex numbers). Suppose a is a limit point of D. If f(x)\rightarrow b as x\rightarrow a, then Re(f(x))\rightarrow Re(b) as x\rightarrow a.

    So we have that if 0<|x-a|<\delta \Longrightarrow |f(x)-b|<\epsilon,
    then, 0<|x-a|<\delta \Longrightarrow |Re(f(x)-Re(b)|<\epsilon.
    However, I'm not sure how to use this to find the apropriate values for epsilon and delta that makes this true. Any help would be appreciated.
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