Equivalently, if (f = u+iv), then (\mathbfV_f = (u, -v)). The Pólya vector field is the conjugate of the complex velocity field (\overlinef(z)). Indeed, (\overlinef(z) = u - i v), which as a vector in (\mathbbR^2) is ((u, -v)).
So (\mathbfV_f) is (solenoidal) — it has a stream function. polya vector field
[ \mathbfV_f(x,y) = \big( u(x,y),, -v(x,y) \big). ] Equivalently, if (f = u+iv), then (\mathbfV_f = (u, -v))
