U=1; h=1; phi=-3.01:0.05:2;
for psi=0:0.1:3.5;
  w=phi+1i*psi; zeta=w/(h*U/pi); sign1=sign(real(w));
  z=(h/pi)*(sign1.*sqrt(zeta.^2-1)+log(zeta+sign1.*sqrt(zeta.^2-1)));
  if(psi==0); hold off; else; hold on; end;
  plot(real(z),imag(z));
end;
axis([-2 2 0 4]); axis square; hold off;