How can I curve fit two curves simultaneously? How can I curve fit complex numbers?
===

More specifically, I am working with a problem where I have gathered experimental data that corresponds to the real and imaginary components of a complex function of the form y(x)= a + b/(x*i) + c/(x+i) + d/(x*i)  [Note:I am using i as the imaginary unit. And I have slightly simplified the function, but not in a significant way].  In other words I have data such that (theoretically) I know y[x1 x2 ... xn] = [t1 t2 ... tn] + [s1 s2 ... sn]*i.  So for any given x value I independently collected experimental data for both the real and imaginary components of y.  
Since both the imaginary and real components of y are dependent on the same parameters (given in the equation above: a,b,c,d) it would be extremely beneficial to be able to curve fit this data simultaneously, or as one unit. 

I have considered:
1) While curve fitting: trying to treat this as one function, where there is some sort of tag or indicator designating 'real' or 'imaginary' which allows the function to output correctly.
2)Curve fitting this as a single a complex function.
3)Curve fitting as two functions, either simultaneously, or in iteratively alternating towards a solution.

I haven't been able to successfully implement any of these ideas. Are any of them possible? Is there another solution which might give me an answer?  Any suggestions on how to proceed?
