>>13337326It's a little more than 2d calculus, it also involves the multiplicative structure of the complex numbers, and the corresponding re-definition of exponentiation, logarithms and roots. That structure adds a lot of rich substance to complex analysis that's not in R^2.
What's hardest really is less about the subject and more about exactly what the course covers, how it's structured, who's teaching it, how prepared you are, and what else is going on in your life. Some complex analysis classes slowly work through half of Schaum's Outline with optional problem sets and fill-in-the-blank exams over a semester in which the students are just taking residual electives in their last year. Some complex analysis classes are dropped on physics students who haven't yet taken real analysis while they concurrently are taking E&M, quantum mechanics, and statistical mechanics, and involve a senile professor chaotically choosing material without reference to a textbook and giving lengthy, cryptic problem sets on a weekly basis.
