I have trouble understanding a whole array of things in complex analysis, which I have basically tracked to the statement "real and imaginary parts of a complex analytic function are not independent."
Because of that, I don't really understand the Cauchy-Riemann equations, the fact that for an analytic function, if its real part is constant, then the whole function is constant, and other fundamental things, such as Cauchy's Integral formula, Maximum modulus principle, etc. (the last two just make zero sense to me.)
The thing is, I pretty much understand the proofs, starting from the beginning, when we define differentiability of a complex function. I don't have any problems with the introduction of complex numbers as well, and different identities.
But I just don't have any intuition for why things are like that, and it's very frustrating, because I always feel like I don't understand complex numbers at all, and just do some standard exercises in class, relying on proven facts that I just assume to be true as a starting point.
But as soon as I go and try to understand the meaning of things we in the class work with, I just immediately stop understanding anything.
Can anyone help me understand why the real and imaginary parts of a complex function are not independent?
from Hot Weekly Questions - Mathematics Stack Exchange
Post a Comment