Since abs(4*z^3+4*c*z) is purely real and %e^%i has a nonzero imaginary
part,
I think the solution set is empty. If I'm wrong about that or if there is a
typo, maybe we can try solving it with to_poly_solve; something like:
(%i10) eqs : [z=z^4+2*c*z^2+c^2+c, abs(4*z^3+4*c*z)=b]$
(%i11) assume(b > 0)$
(%i12) to_poly_solve(eqs,[z,c]);
(%o12) [[z=-sqrt(b)/2,c=-(b^(3/2)+2*b)/(4*sqrt(b))], ... ]
Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>I'm trying to solve system of equations for c:
>
>z=z^4+2*c*z^2+c^2+c
>abs(4*z^3+4*c*z)=%e^%i
>
>It should have 1 complex solution.