Partitions on C = {i,-1,-i,1}

Question

Let $ C = \{i, -1, -i, 1\}$ , where $ i^2 = -1 $. The relation $R$ on $C$ given by $xRy$ iff $xy = \pm 1$ is an equivalence relation on $C$. Give the partition of $C$ associated with $R$

I would really appreciate any help. I am not really sure where to start with this. Is it as simple as the partition just containing 1 and -1.

Thank you very much.

Answer 1

The equivalence classes are the classes that fulfill that relationship, then your classes must partition C. Note that $C_i = \{i,-i\}$ and $C_1=\{1,-1\}$ do this so these are your classes. If you took any element in $C_i$ and one in $C_1$ and multiplied them you would not get $\pm 1$ so they are not in the same equivalence class.