Finding the equivalence class of a relation |a| = |b| For the following relation $R$ on the set $X$ determine whether it is $(i)$ reflexive, $(ii)$ symmetric and $(iii)$ transitive. Give proofs or counter examples. In the case where $R$ is an equivalence relation, describe the equivalence classes of $R$.
$X=\mathbb C,\; a\;R\;b\iff |a|=|b|$
$(i)$ The relation is reflexive since $|a|=|a|$ is true
$(ii)$ The relation is symmetric as if $|a|=|b|$ then $|b|=|a|$
$(iii)$ The relation is transitive if $|a|=|b|$ and $|b|=|c|$ then it follows that $|a|=|c|$
And this is as far as I get. I am struggling when it comes to identifying an equivalence class for this relation. I honestly don't even think I'd know where to begin for this. A nudge in the right direction would be greatly appreciated.

Hint:
You can find the answer if you think to complex number $a$ in polar form $a=|a| e^{i\theta}$. than you have an equivalence class for any value of $|a| \in \mathbb{R}$.
