Thread: Limits of Function with complex numbers

1. Limits of Function with complex numbers

I am studying for an exam and came across this excercise...
Let $\displaystyle f: D\rightarrow C$
(complex numbers). Suppose a is a limit point of D. If $\displaystyle f(x)\rightarrow b$ as $\displaystyle x\rightarrow a$, then $\displaystyle Re(f(x))\rightarrow Re(b)$ as $\displaystyle x\rightarrow a$.

So we have that if $\displaystyle 0<|x-a|<\delta \Longrightarrow |f(x)-b|<\epsilon$,
then, $\displaystyle 0<|x-a|<\delta \Longrightarrow |Re(f(x)-Re(b)|<\epsilon$.
However, I'm not sure how to use this to find the apropriate values for epsilon and delta that makes this true. Any help would be appreciated.

2. You have post some serious problems.
http://www.mathhelpforum.com/math-he...ial-19060.html
So Why not learn to post in symbols? You can use LaTeX tags.
Let $\displaystyle f: D\rightarrow C$
(complex numbers). Suppose a is a limit point of D. If $\displaystyle f(x)\rightarrow b$ as $\displaystyle x\rightarrow a$, then $\displaystyle Re(f(x))\rightarrow Re(b)$ as $\displaystyle x\rightarrow a$.
So we have that if $\displaystyle 0<|x-a|<\delta \Longrightarrow |f(x)-b|<\epsilon$,
then, $\displaystyle 0<|x-a|<\delta \Longrightarrow |Re(f(x)-Re(b)|<\epsilon$.