= Solution
A <uniform flow> with physical <velocity> $(U\cos\alpha,U\sin\alpha)$ has <complex velocity> $Ue^{-i\alpha}$ and incident potential $f(\zeta)=Ue^{-i\alpha}\zeta$. Apply the <Milne-Thomson circle theorem> with $R=1$:
$$
\boxed{W(\zeta)=U\left(e^{-i\alpha}\zeta+\frac{e^{i\alpha}}\zeta\right).}
$$
Indeed, on $\zeta=e^{i\theta}$ it is $W=2U\cos(\theta-\alpha)$, which is real, so the boundary is a <streamline>. At infinity, $W'(\zeta)\to Ue^{-i\alpha}$, verifying the specified incoming <uniform flow>.
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