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Math Help - Need some help with complex functions... :(

  1. #1
    Junior Member
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    Unhappy Need some help with complex functions... :(

    hello
    I'm having big problem with simple issue, so if any one is willing to guide me to the right approach I will be most grateful

    my problem is with this task

    "If complex function f(z) is regular in the area D\subset \mathbb{C} than it's also continuous on same defined area."

    and I need to prove it but i can't even start it because if I assume that some function is regular that implies that function is continuous.... !?!??! I have no clue how to do this
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    For every z_0\in D :

    f(z)-f(z_0)=\dfrac{f(z)-f(z_0)}{z-z_0}\cdot (z-z_0)\;,\;(z\neq z_0)

    Taking limits when z\rightarrow z_0 :

    \displaystyle\lim_{z \to z_0}{(f(z)-f(z_0))}=f'(z_0)\cdot 0=0

    Now, you can conclude.


    Fernando Revilla
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  3. #3
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    Thank you very very much
    (I'm an idiot hehehehehe)
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by sedam7 View Post
    (I'm an idiot hehehehehe)

    Welcome to my Club.


    Fernando Revilla
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