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Solving an equation

I have an equation, Gamma[a+I b] = some complex number.  I need to
solve this equation for a and b.  I can write a+I b as z, but it can't
be solved through NSolve.  What I have been doing is a double do loop
for a and b and getting some number.  Then I compare this to the
number I have.  Then I narrow down my possibilities for a and b, and
go through the process again.  Does anyone know of a better way to do
this problem?  Is there a way to have Mathematica compare each result
of the do loop to a given value, and given certain conditions spit out
an answer for a and b?

Hope that makes sense.

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