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?