Show that holomorphic function $f: \mathbb{C} \rightarrow \mathbb{C}$ is constant Let's $f: \mathbb{C} \rightarrow \mathbb{C}$ be a holomorphic function such that values $f$ are on line $y=ax+b$. Show that $f$ is constant.
I think I should use Cauchy-Riemann equations but I don't know what does mean that values $f$ are on line $y=ax+b$. Can you explain me that?
Thanks in advance.

Herewith my second answer:
Holomorphic functions are conformal except where their derivatives are zero.  It can't be conformal if its image is a straight line.
