A Question 1: Prove that given 4 distinct points 31,22, 33, 34 E C = C U {so} that the cross ratio [21, :52, 33, a4] is a real number if and only if the points are either collinear or cocircular. Question 2a: Let M(a] : E. Draw a circulation diagram for M. Does the notion of 'sink' or 1source1 make sense at the xed points? 2b: Show that a Mobins transformation that takes the upper half plane H lzaijectitrelj,r to itself must be of the form :1; where a, b, cid are real and ed be I? U. Question 3: The word circle in this problem will refer to a traditional circle as well as circles that go through innity a.k.a lines. Show that the composition of two reections over two suc- cessive circles is a Mobins transformation. You can do this directly from the formulas for reections as discussed in class as well as the natural equations of lines and circles in the complex plane? nothing complicated about this problem! Question 4: Let D = {z : |z| <1: p