Change of Variables & the Jacobian · Medium problem

The map $x = u^2 - v^2$, $y = 2uv$ (squaring $z = u + iv$ as a complex number) sends a tiny counterclockwise loop around $(u,v)=(1,-1)$ to a tiny loop around its image. Compute the Jacobian determinant there, and state whether the image loop is traced counterclockwise or clockwise.