Solving these set of equations

For $${a,b,c}in mathbb{C}$$ and $${gamma,N}in mathbb{Z}^+$$, I have an equation

``````eq(c_, Ν_, γ_) := ((b - (I c)/2 + a γ) ((-1 +
b - (I c)/2 + a γ)/(-1 + b + (I c)/2 +
a γ))^(-1 + Ν))/(b + (I c)/2 + a γ) + (
Gamma(1 - (I c)/a - γ) Gamma(
1 + (I c)/a - γ + Ν/2))/(
Gamma(1 + (I c)/a - γ) Gamma(
1 - (I c)/a - γ + Ν/2))
``````

Now, I want to find $${a,b}inmathbb{C}$$ numerically, because doesn’t look like it can solve analytically. So I wanted to try something like

``````NSolve({eq(0.3+0.1I,6,1)==0,eq(0.3+0.1I,6,2)==0},{a,b})
``````

But this ran forever and gave me no result. Is there a way to make it solve for this?