This applet helps with visualization of elementary complex functions as transformations of the plane. You can drag a unit square around the domain on the left and observe its image under the transformation in the codomain on the right. The domain and range windows are fixed to [-2,2]x[-2,2] and show the unit circle for reference, but this suffices for illustrating the transformation properties of several of the standard examples. The default example is f(z)=z^2, but you can enter other transformations as well.
