= Solution
Writing $\zeta=\xi+i\eta$,
$$
u-iv=\frac1{\zeta+2}=\frac{\xi+2-i\eta}{(\xi+2)^2+\eta^2}.
$$
Therefore
$$
\boxed{\mathbf u=\frac{(\xi+2,\eta)}{(\xi+2)^2+\eta^2},\qquad |\mathbf u|=\frac1{\sqrt{(\xi+2)^2+\eta^2}}.}
$$
The <vector field> points radially \b[away from $(-2,0)$], with magnitude inversely proportional to distance from that point. It diverges on approach to that boundary point and tends to zero far away. This is the radial <potential flow> described by the logarithmic <complex potential of a two-dimensional potential flow>.
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