# Upper Half-plane Model Assignment | Assignment Help Services

Let A = (1, 2) and B = (2,√3) be points in the upper half-plane model. (As complex numbers A = 1 + 2i and B = 2 + i√3.)a) Find the ‘endpoints’ E1 and E2 of the hyperbolic line that contains A and B.b) Draw a sketch of the hyperbolic line that contains A and B.

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c) Compute the cross ratio (E1,A;B,E2).d) Find the hyperbolic distance dhyp(A,B).#2. Again, let A = (1, 2) = 1 + 2i and B = (2,√3) = 2 + i√3. Let T be the transformationT(z) = −1/za) Compute the images T(A), T(B).b) Plot the points T(A) and T(B), and sketch the hyperbolic line that passes through them.c) Compute dhyp(T(A), T(B)); check that this distance matches your result in 1d).

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