= Solution
{c}
The <Joukowski map> is a <holomorphic function> for $z\ne0$, with
$$
g'(z)=1-\frac1{z^2}.
$$
A <holomorphic function> is a local <conformal map> wherever its <derivative> is nonzero. Hence the two finite nonzero critical points are
$$
\boxed{z=1,\qquad z=-1}.
$$
They lie on the boundary of the fluid region. At $z=0$ the displayed formula has a <pole> and is undefined as a map to the finite <complex plane>; zero is outside the fluid region. Thus $g$ is locally <conformal> everywhere in the fluid.
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