Solution
= Solution
{c}
The <line vortex> is mapped to
$$
\boxed{\zeta_0=g(c)=c+\frac1c}.
$$
Its <imaginary part> is positive because $c$ lies in the fluid region. A <conformal map> preserves the <circulation> of the local <line vortex>, so its strength in the mapped <complex plane> is still $\Gamma$.