Is Complex Analysis comparatively more difficult than other areas of mathematics?
That’s really subjective, although analysis in general tends to be a notoriously difficult subject for first-timers. However, a first course in real analysis tends to involve a lot more rigor than a first course in complex analysis. The reason for this is because by the time you take real analysis, you would have already taken the fundamental calculus courses (differential, integral, and vector/multivariable). These courses only cover calculus on functions of a real variable, so by the time you get to real analysis, you are already comfortable with the basics, and are ready to move on to the more rigorous side of the subject. On the other hand, most people don’t learn how to perform calculus on functions of a complex variable until they reach their first complex analysis course. Fortunately, a lot of it is very similar to vector calculus (many of the same techniques are used) so it doesn’t take as long to learn. However, because you still have to cover the basics, a one-semester course
