I'm trying to demonstrate the quantum mechanical identity
((I a -1)/(I a + 1))^(i b) == Exp[ - 2 b Arccotangent[a]]
and have thus far had no luck. My professor isn't familiar with Mathematica, and claims ''Maple just does it.'' I tried a ComplexExpand on the left hand side and got nowhere close to what I was looking for. Any guidance would be much appreciated.