Complex Variables Problem Set :
If w_1 = w_1 (Z) = a_1 Z + b_1/C_1 Z...
If w_1 = w_1 (Z) = a_1 Z + b_1/C_1 Z + d_1, w_2 = w_2 (Z) = a_2 Z + b_2/C_2 Z + d_2, then w_1 w_2 (Z) = w_1 c w_2 (Z)) is also a bilinear transformation. if w_1 (Z), w_2 (Z), w_ (Z) are bilinear transformation, the w_1(w_2 w_3 (Z)) = (w_1 w_2) w_3 (Z) for any bilinear transformation w_1 (Z), there exists that w_1 (w_2 (Z)) = w_2 c w_1 (Z)) = Z bilinear transformation w_2 (Z) such that say that the bilinear transformations from a group under composition: show that this group is not commutative by finding two bilinear transformations w_1 (Z) and w_2 (Z) such that w_1(w_2 (Z)) w_2 (w_1 (Z)).