That is exactly what it is! In the real plane you get exponential growth: the rate of change is equal to the current value. In the Argand plane you get a curl

That is exactly what it is! In the real plane you get exponential growth: the rate of change is equal to the current value. In the Argand plane you get a curling action due to the quadrature effect of the imaginary unit. The rate of change at each point is the tangent, and the result is therefore a circle. Lie infinitesimal displacements capture this nicely, and also render the generic case which is a similarity transformation, e.g. rotation through two half reflections, e^(-w/2) * x * e^(w/2) like those found in quaternions and Clifford algebras.