Let $f: G \to \mathbb C$ be an analytic function which is constant on a disk. Then $f$ is constant on whole of $G$, where $G$ is an open connected set.
I was reading complex analysis and there they are using the abovesaid thing again and again without giving any explanation to this. I think this is something very elementary but I am not able to get this.
Any help will be appreciated. Thanks.