Question

Non Euclidean Geometry Show that if z=x+yi with y>0, then |U(z)|<1, where U(z)= (iz+1)/(z+i)

Non Euclidean Geometry

Show that if z=x+yi with y>0, then |U(z)|<1, where U(z)= (iz+1)/(z+i)

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Answer #1

Note that for this to be true one need as take , then , and , then . o one need to assume also.

, Note that

Now to show it is enough to show or , as .

Note that (as ) (as )

Thus we have .

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