A2 - ) and that the identity is a mobius transformation....

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MATH185: Assignment 2 1. Assume a, b, c, d are complex numbers such that ad - bc 6 = 0. Consider the function f : ˆ C ˆ C given by f a,b,c,d ( z ) = az + b cz + d if z 6∈ {- d c , ∞} if z = - d c a c if z = these functions are called mobius transformations. (a) Show that the function f a,b,c,d is continuous and that it extends the function az + b cz + d : C - - d c C (b) Show that the composition of two Mobius transformations is also a mobius transformation. (c) Show that the inverse of the mobius transformation f a,b,c,d ( z ) is f d, - b, - c,a ( z
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Unformatted text preview: ) and that the identity is a mobius transformation. (d) Construct a Mobius transformation which maps three given dis-tinct numbers z 1 , z 2 , z 3 in the extended complex plane to the points 0 , 1 , . (e) Using parts ( c ) and ( b ) show that, given complex numbers z 1 , z 2 , z 3 , w 1 , w 2 , w 3 in C there exists a Mobius transformation which maps z i to w j . 2. Section 19: 2,3,4,8,9 3. Section 22: 2,3.6,7,8 1...
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