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Bringing T into the fundamental domain.
Let T = (9 + i )/ 10.Find the transformation in the modular group that brings it into a point To of the fundamental domain :F0 • Show that the transformation is unique by proving that there is no transformation in the modular group (except the identity) that leaves To fixed. Partial answer: To = 5i . Repeat the above computations for T = 9/ l O + i / l 00. Partial answer: To = i + 1/ 10. [Hint: Use the procedure discussed in the proof that any T can be brought into the fundamental domain.]
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