B Let S = C and let G = { Ro(z) = ei= | 0 = R} . Prove that G is a transformation group. (The geometry ( S, G ) is called rotational geometry.) . Let D = fall lines in C). This is an invariant set in rotational geometry because rotations take lines to lines. Partition D into its minimally invariant sublets. [Hint: start with a specific line like > = 1 and compute its orbit. Is there a nice way to describe all of the lines in the orbit of a = 1?] . Describe the minimally invariant set containing the circle C' of radius 4 centered at 2 + z in rotational geometry. . Let C be the set of all circles in C. This is an invariant set in rotational geometry because rotations take circles to circles. Find a non-constant invariant function on C. . Is rotational geometry homogeneous? Isotropic