Consider a complex number in rectangular form, i.e. $z=x+iy$. If I am given the real part and imaginary part of the function, take $z^2$ as an example, i.e. $f(z)=z^2=(x^2-y^2)+i(2xy)$. Is it possible for me to have a systematic way to find out the original function? (i.e. $f(z)=z^2$)
I don't know whether it is a silly question, or the answer can be found easily from google. So any related link or generous response will mean a lot to me!