I understand that the modulus of a complex number $z=x+iy$ is the square root of $x^2+y^2$, but what is the modulus of a complex function $f(z)=u+iv$ where $u$ and $v$ are functions in the reals? Specifically, what is the formula for $|f(z)|$ where $f=u+iv$? And could you add a few notes on what the modulus of $f(z)$ represent?