Hi i got problem cant find isomorphic function between this groups:

G=[{1, -1, i, -i}, *] and [Z4, +4]

first group is defined with normal multiplication, second is cyclic Z4 group with mod 4 addition, here is what i thought of:

since i need to convert * op to + op has to do something with Log function cause the groups must be closed under the op. and the function that i must find has to be homomorphic: kinda f(x) = Log(x), so for check on closed property i get x and y E in G and f(x*y)=Log(x) + Log(y), the problem is when i need to get f(-1) or f(-i) since under the log there cant be negative or else i get another complex number but in Z4 there's no complex numbers.. so im confused here i cant find the function.. any help would be appreciated thanks