Calculate carefully to show that the "Poincare metric" ((Euclidean metric)/(1-r²)) on the unit disc {z: |z| <1 , zC} is "invariant under T_a, T_a(z)= (z-a)/(1-z).

T_apreserves Poincare length of infinitesimal displacementz.

Find the Poincare length of the curve in (t) = t+ 0i t [0,r] 0