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Prove the formula F(z)=2z/1+|z| squared for the isomorphism F of the Poincare model onto the Klein model. What is the formula for the inverse isomorphism?

Prove the formula F(z)=2z/1+|z| squared for the isomorphism F of the Poincare model onto the Klein model. What is the formula for the inverse isomorphism? Angle measure in the Klein model is defined so that F preserves angle measure; draw the diagram which illistratesthis.

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