\[g(z)=e^{-\pi i/4}(2\sin\alpha)^{-1/2}\left(e^{-i\alpha}-z\right)^{-1/2}+e^{\pi
i%
/4}(2\sin\alpha)^{-1/2}\left(e^{i\alpha}-z\right)^{-1/2}.\]