Let P be the point that corresponds to z.
The point Q that corresponds to the complex number zw is obtained by
1) scaling of the distance OP by the factor k, followed by,
2) rotating the point P anticlockwise about the origin through the angle
If k < 0, then scaling of distance from the origin by a factor of |k| will be in the opposite direction.
My issue: this is from some notes I have from school and I don't understand the last sentence. What does it mean, "scaling of distance will be in the opposite direction"?
If k<0 then write
then use that
and you get your original case with
which, of course, means you scale by |k| and the
bit of the angle forces you another 180 degree rotation, which is in the opposite direction of the original.