= Solution
{c}
A uniform horizontal <velocity potential> in the upper $Z$-plane is a real constant times $Z$. Since $dz/dZ=(2/\pi)R/Z$, choose
$$
\boxed{w(z)=\frac2\pi Z(z)}
$$
up to an additive constant. Its <complex velocity> is
$$
\frac{dw}{dz}=\frac ZR.
$$
As $Z\to\infty$ this tends to one, giving physical <velocity> $(1,0)$. As $Z\to0$, $R\to i$ and $Z/R\to0$, giving zero <velocity> far down the channel. The <imaginary part> of $w$ is constant on the real $Z$-axis, so the physical boundary is a <streamline> and the impermeability condition holds. The usual <complex velocity> convention is $dw/dz=u-iv$.
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