What is the Jacobian of the function $f(u+iv)={u+iv-a\over u+iv-b}$?
I think the Jacobian should be something of the form $\left(\begin{matrix} {\partial f_1\over\partial u} & {\partial f_1\over\partial v} \\ {\partial f_2\over\partial u} & {\partial f_2\over\partial v} \end{matrix}\right)$
but I don't know what $f_1,f_2$ are in this case. Thank you.