There's a theorem (on p. 64 of Gamelin, for example) that says the following:
Given any three distinct points in the extended complex plane, and given any three distinct values in the extended complex plane, there is a unique fractional linear transformation [Ackbeet: Mobius transformation] such that and
So, applying this to your situation, the Mobius transformation is completely determined by the equations:
z=-1 -> w=infinity
z=0 -> w=i
z=1 -> w=0
My guess is that, once you've found that transformation, you'll find that i maps to the number they say. Does that help?