I had some trouble with this problem:
Is isomorphic to { } ?
I made product tables but I'm having a hard time identifying the isomorphic relationship. Is there one?
If I understand correctly your symbols, we have two cyclic groups of order 4, one written additively (addition modulo 4) and the other one written multiplicatively (complex multiplication). Identify a generator in each and define a map between these two generators, mapping powers of one to powers (or multiples) of the other...
Tonio