Complex Mapping of Parametric Curve

Image of the parametric curve [math]x(t) + iy(t)[/math] under the complex mapping [math]u(x,y) + i v(x,y)[/math]. Drag the time slider and input the appropriate functions. The blue curve is the parametric and the red curve is the image under the complex mapping. The arrow shows there the leading point of the parametric curve is mapping to.