So we just talked about the cauchy riemann equations and had the example $f:\mathbb{C} \rightarrow E$ where $E$ is the disk $E= \lbrace z \in \mathbb{C} : \mid z \mid \leq 1 \rbrace$ and f differentiable. Then $f$ has to be constant. But why?
However I do understand why $f$ has to be constant when $Re(f)$ or $Im(f)$ is constant with cauchy riemann equations.