Hello! I see that all theorems in complex analysis are talking about a function in a region of the complex plane. A region is defined as an open, connected set. If I am not wrong, the real line, based on this definition, is a region. I am a bit confused why there are so many properties of the complex functions that we don't have in the real ones, if the real line is just a particular case of the most general one (a region in the complex plane)? Thank you!