Linear equations having complex terms optimization

I have equations like

c = (a+ib)*x(1)^2 +( b+ic)*x(2)^2 -50

ceq=[]

Can this be solved by nonlinear constraints?

I am having errors of out of bound

[Walter Roberson]

Is that the same c on the left side as the c in the ic term?

Those are not linear equations in x. Are you solving for something other than x ?

[Avishek Banerjee]

Sorry the left side c is the [c, ceq] term in the nonlinear constraint model

[Walter Roberson]

I am not clear as to what the constraint is? For some parameters a, b, c, you want to test (a+i*b)*x(1)^2 + (b+i*c)*x(2)^2 - 50 <= 0 ? If x(1) and x(2) are particular complex numbers, that equation would tend to have real and imaginary components: it does not make sense to test whether a complex value is greater than or less than 0 ?