# Thread: Looking for a special function +_o

1. ## Looking for a special function +_o

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

Perhaps none of the elementary functions do not satisfy my requirement ...since i have checked them

2. Hi,
Originally Posted by simplependulum
Is there a continous , single-valued function $\displaystyle f(z)$ which has a property $\displaystyle f(\overline{z}) \neq \overline{f(z)} ~~ \forall z \in \mathbb{C}$ ?
Let $\displaystyle f:z\mapsto i$. This function is obviously continuous and for all $\displaystyle z\in\mathbb{C}$ we have $\displaystyle f(\bar{z})=i$ and $\displaystyle \overline{f(z)}=-i$ hence $\displaystyle f(\bar{z})\neq \overline{f(z)}$.