In the plane A2, with respect to the standard affine frame, appoint of coordinates (x,y) can be represented as the complex number z = x + iy. Consider the set of geometric trans formations of the form...

In the plane A2, with respect to the standard affine frame, appoint of coordinates (x,y) can be represented as the complex number

z = x + iy. Consider the set of geometric trans formations of the form

 where a, b are complex numbers such that a=0. (a)Prove that these maps are affine. Describe what the se maps dogeometrically.

(b) Prove that the above set of maps is a group under composition.

(c) Consider these to f geometric trans formations of the form
where a, b are complex numbers such that a=0, and where z=x−iy if z=x+iy. Describe what these maps do geometrically. Prove that these maps are affine and that this set of maps is a group under composition.