II.7.1 Compute explicitly the fractional linear transformations determined by the following correspondences of triples (a) (1+i,2,0)(0, , i-1) (b) (0,1,) (1,1+ 1,2) (e) (1,2,) (f) (0, 0, i) (0,1,) (0, 1,) (c) (o, 1+1,2)(0, 1,) (g) (0, 1,) (0,, i) (d) (-2.1.2) (1-21,0,1+2i) (h) (1,i,-1) (1.0, -1) Solution (a) We have the points (w-w) (ww) (w-w2) (ws-wo) - = (2-20)(21-22) (2-22) (21-20) = 20 1+i 2 = 2 12=0 wo = 0 W = x0 W=i-1 The mapping is (w-wo) (1-w/w) (w-w2) (1-wo/w) take limit as w , to obtain = (220) (21-22) (222) (21-20)" (x-(1+i)) (2-0) 2iz+(2-2i) W=