fsolve accuracy with complex variables [SOLVED]

[JMB]

The following equation:

|x|^2-200*x+500+500*i = 0 (eq1)

where x is a complex variable, can be solved splitting it into two separate equations, one for the real part and another for the imaginary part. Applying this method, one gets the solution:

197.43587635+2.5*i (sol1)

Substituting sol1 into eq1, gives the exact value 0. Now, I was trying to solve this same equation using the function fsolve:

fsolve(|x|^2-200*x+500+500*i,x,190+i)

The calculator (firmware 8051) returns the value:

197.501663563-2.56405881565*i (sol2)

Trying different initials guesses leads to the same solution. The real parts of sol1 and sol2 are quite close, but not the imaginary parts.

Also: ABS(sol1)-ABS(sol2) = -0.066603127, and ARG(sol1)-ARG(sol2) = 2.56433999704E-2 (in radiants). So, depending on how you look at it, the solution given by fsolve is not so bad.

Does anyone know how to improve the calculator's accuracy?