Need some help with complex functions... :(

**sedam7** · January 23rd 2011, 03:18 AM

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

**FernandoRevilla** · January 23rd 2011, 03:26 AM

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

**sedam7** · January 23rd 2011, 03:38 AM

Thank you very very much

(I'm an idiot hehehehehe)

**FernandoRevilla** · January 23rd 2011, 03:44 AM

Originally Posted by sedam7

(I'm an idiot hehehehehe)

Welcome to my Club.

Fernando Revilla

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