Where i=sqrt(-1), either would do.
Without proper constraints, the problem is trivial. The fact that the variable is called 'n' means nothing.
OTOH, if f is integer-valued and of an integer variable,
f(0)=0
f(2n)=-(2n-1)
f(2n-1)=2n
f(-(2n-1))=-2n
f(-2n)=2n-1
The difficult one is f(f(n))=n^2.
2) You can't just do an operation to the right side and then do the inverse inside of the function on the left side. It has to be done outside of the function.
3) You didn't accomplish anything with your butchered math. We wanted f(f(n)) = -n
Given z a non-zero integer, either z=2n or z=2n-1 or z=-2n or z=-(2n-1), for some natural n>0... f(n) is defined according to each case. Uhu? And AFAIK f(f(n))=-n.
This should not be too hard to express in 32 bit arithmetic. With bitwise shifts etc.
f(n)
= abs(n) + 65536 if n < 65536
= unsigned32(n & 0xffff) ** 2 if n >= 65536
I know, I should have read the OP but I was too lazy.
Really cheeky, though :)
I leave that as an exercise to the reader. :-)