A question about vortex with complex potential

I found this exercise from text book:

5. Consider a $2 mathrm{D}$ vortex with complex potential
   $$
   W(z)=frac{i}{2 pi} ln (z-1)
   $$
   i) Compute the circulation around the loop $Gamma$ given by the algebraic equation $x^{2}+y^{2}=frac{1}{2} .$ ii $)$ An infinitely long impermeable wall is placed along the $y$ axis. Determine the new complex potential of the vortex that accounts for the presence of the wall. Plot the streamlines and potential lines. iii) Compute the velocity vector at $(x=0, y=0)$

This is similar to what we discussed from class, a vortex flow but with different $z$, that is, we introduced complex potential for vortex is given by
$F(z)=-i c log z$ , here the problem used $z-1$ instead of $z$. How to correctly understand this change of complex variable?

My approach is to treat new origin as $(1,0)$, is that correct?

Any help or hint is appreciated.