I think that I have three independent equations because I have known |Z|, Real and Imaginary part and Re, Ri and C are unknown. Relationship between |Z| and (Real, Imag) is |Z|=sqrt(Real*Real+Imag*Imag) so I have to have set of solutions (Re, Ri, C) which will satisfy |Z|, Real and Imag but not |Z| and sqrt(Real*Real+Imag*Imag).
Explanation:
Real=300
Imag=-400
|Z|=sqrt(300*300+400*400)=500
but
Real=300
Imag=400
|Z|=sqrt(300*300+400*400)=500
will give the same value for |Z| and no for Imag.
Am I correct?