system of equations



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.


I have tried :

algsys([z=z^4+2*c*z^2+c^2+c, abs(4*z^3+4*c*z)=%e^%i], [c]);

gives no solutions.

Is it possible in Maxima ?

Adam