Question 1 [ 12 marks]: (a) [4 marks] Find the direct isometry R from the complex plane to the complex plane which maps the point 1 to point i, and maps (1+i) to (-1+i). Classify the isometry R. (b) [4 marks] Find the indirect isometry T from the complex plane to the complex plane which is the reflection across line l passing through points (1+i) and (2-i). (c) [4 marks] Let S be an affine function S(z) = mz + n from the complex plane to which maps the points A, B, C to the points D, E, F respectively. Show that triangles ABC and DEF are similar.