You will need a theoretical analysis first because:
1. solve may omit solutions
2. f (z,A,phi) has values arbitraryly close to 0 (by Casorati–Weierstrass theorem).

BTW. It's not a good idea to use Zeta as variable (it's reserved for Riemann's function). 

@Carl Love  It would be interesting a 10 minutes contest: given Count, explain what it does and how it works.

.maple files are not accepted by mapleprimes. Use .mw or compress into a .zip.

@Rouben Rostamian  Yes, it's a vector graphics, but I suspect that it was produced from a bitmap.
In Maxima the EPS is obtained in a second and has 200KB.

@Rouben Rostamian  In Windows, exporting 3d graphics to EPS does not work well at all.
For example 

p:=plot3d([x^2+y^2,1-x^2-y^2], x=-1..1,y=-1..1);
plottools:-exportplot("d:/tmp/aatest.eps", p);

 needs several minutes, has 12MB and artifacts.
It is probably a vectorized version of a bitmap. Useless.

@mmcdara In Maple 2020+

sort(1+x,descending):
# ...
g := x -> 1/(1+x):
(g@@3)(x);

@Carl Love You wrote  "Because the module references are linked into the code at the time that the code is read, not the time that it's executed".

But when uses IM is parsed, IM was already parsed, so the exports are known and it would be enough for the parser to "observe" that add_three is exported by IM and to add the IM:- prefix.
I don't see any reason to reject uses IM.

@mmcdara 

1. I think that this can be set with the Typesetting package, e.g. with the interactive Typesetting[RuleAssistant]()
I do not use it much. Anyway, after with(Logic) the desired typesetting is automatic.

2. A name beginning with & is treated as a binary operator (or prefix unary). See ?neutral operators

@greatpet I don't know why uses does not work in this form. But it does with "equations" (which is actually more clear and allows abbreviations):

restart;
OM := module()
option packge;
export IM:= module()
    option package;
    export add_three := x-> x+3;
    end module;
export times_two_add_three:= 
  proc(x)
    uses k=IM;
    k:-add_three(2*x);
  end;
end module:
OM:-times_two_add_three(z);

@greatpet with cannot be used inside modules and procs. Use the uses clause instead.

@greatpet You may simply write

export procedure1 := IM1:-procedure1;
etc.

E.g. in Carl's example:

restart;
OM:= module()
option package;
export
    IM:= module()
    option package;
    export add_three:= x-> x+3;
    end module;
export add_three:=IM:-add_three;
end module:

with(OM);
#                        [IM, add_three]

add_three(z);
#                             z + 3

@mmcdara Yes, I wanted minimal modifications of the previous answer (for ratpoly).
The unpleasant fact is that solve finds only the solutions with c=0.

@tomleslie Actually I was aware that Excel throws an error for x*m<0 but I don't understand why and I have preferred the simplicity. After all, we may say: Excel is unable to compute MROUND(x,m) when x*m<0.

@mmcdara Merci. For my native Romanian the term is perfect :-)

I am not sure whether this is the right forum for such questions. Better choices could be https://math.stackexchange.com or https://mathoverflow.net. A CAS cannot help much when a proof needs more or less special theorems/formulae to be applied. For example, Maple cannot manage the limit of a sequence: limit(h(n), n = infinity) assuming n::even.