Consider the following transformation az + b w = A= ad – bc # 0 cz + d' a) Show that the map can be inverted to find a unique (single valued) z as a function of w everywhere. b) Verify that the mapping can be considered as the result of three successive maps: a z' = cz + d, z" = 1/z', z" + %3| W = - where c + 0 and is of the form b w = d when c = : 0.

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