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Complex Solutions in a bounded region (two equations)

Hi All,

I'm trying to find all the solutions in a bounded region of the
complex plane of a couple of equations (which in principle involve
transcendental equations, but they could be more complicated), i.e all
the zeros of

f1[z1,z2]==0 and f2[z1,z2]==0

with z1 and z2 complex numbers.

I came across with the ZEAL package, that worked very well for my
purposes but only accept one equation, and I'm trying with FindRoot
without too much success (choosing different starting points,
splitting the domain, etc.). Also I've tried Reduce but it is enable
to manage this system of equations (in a similar problem with only one
equation I was able to get all the solutions).

Does anybody know what I could try?

Thanks in advance for your help,

Marcelo Ciappina
Research Fellow
ICFO - The Institute of Photonics Sciences
Barcelona, Spain

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