# Thread: Need some help with complex functions... :(

1. ## 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 $\displaystyle f(z)$ is regular in the area $\displaystyle D\subset \mathbb{C}$ 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

2. For every $\displaystyle z_0\in D$ :

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

Taking limits when $\displaystyle z\rightarrow z_0$ :

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

Now, you can conclude.

Fernando Revilla

3. Thank you very very much
(I'm an idiot hehehehehe)

4. Originally Posted by sedam7
(I'm an idiot hehehehehe)

Welcome to my Club.

Fernando Revilla