Problem:
Let $f$ be defined as $f(z)=\frac{z}{1+|z|}$. Is $f$ continuous from $\mathbb{C} \to \mathbb{C}$?
Progress:
$f$ is clearly well-defined on $\mathbb{C}$, but is not holomorphic (Cauchy-Riemann equations are not satisfied as a result of the '$|z|$' term).
I think we may need to make use of the '$\epsilon$-$\delta$' definition of continuity but I'm really not sure how to apply this to complex-valued functions. Any assistance would be very appreciated.