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.