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