I have some question when reading Complex analysis by Ahlfors.
Why analytic functions are true functions of a complex variable as opposed to functions which are more adequately described as complex functions of two real variable? I understand that the $\frac{\partial{f}}{\partial{\bar{z}}}=0$, but I still can not understand this sentence.
The following seems to give a method to compute the conjugate harmonic function of $u(x,y)$. I don't know what means $\bar{f}(z)$, is it be made by conjugate the coefficient? And I do not know Why " $f(z)$ is only determined up to a purely imaginary constant."
I am really confused with this page, could you get me some reference(I have searched in Google but can not get a proper one) or answer my confusion? Thank you very much!