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Math Help - Looking for a special function +_o

  1. #1
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    Looking for a special function +_o

    Is there a continous , single-valued function  f(z) which has a property  f(\overline{z}) \neq \overline{f(z)} ~~ \forall z \in \mathbb{C} ?

    Perhaps none of the elementary functions do not satisfy my requirement ...since i have checked them
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi,
    Quote Originally Posted by simplependulum View Post
    Is there a continous , single-valued function  f(z) which has a property  f(\overline{z}) \neq \overline{f(z)} ~~ \forall z \in \mathbb{C} ?
    Let f:z\mapsto i. This function is obviously continuous and for all z\in\mathbb{C} we have f(\bar{z})=i and \overline{f(z)}=-i hence f(\bar{z})\neq \overline{f(z)}.
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