partial derivative with respect to z & z_bar?? Hi, all.. While I`m reading the Ahlfors` complex analysis..I`ve found a tricky expressions about partial derivatives.. On the theory of analytic fns. author uses the expressions ∂f/∂z , ∂f/∂z_bar (z_bar - complex conjugate) with f=f(x,y)(f is a complex fn of two real variables..) by introducing z=x+iy, z_bar=x-iy as new "independent" variables.. By the way, can z and z_bar be independent? Moreover, if we write f(z,z_bar) instead, the expression ∂f(z,z_bar)/∂z seems to be misleading in a sense that the conventional definition of partial derivative tells us that z_bar must be fixed while z varies ( which cannot be) Can anybody give me an answer for this?