Explore the transformations and comment on what you find.
Follow hints using a little coordinate geometry, plane geometry and
trig to see how matrices are used to work on transformations of the
Choose some complex numbers and mark them by points on a graph.
Multiply your numbers by i once, twice, three times, four times,
..., n times? What happens?
Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.