= Solution
For nonzero <complex numbers>, $x\overline y=(x/y)|y|^2$. Since $|y|^2$ is positive real, the condition is equivalent to $x/y\in\mathbb R\setminus\{0\}$. \b[This is an <equivalence relation>.] The ratio $x/x=1$ gives <reflexivity>; the reciprocal of a nonzero real ratio shows that the relation is <symmetric>; and $(x/y)(y/z)=x/z$ gives <transitivity>. An <equivalence class> is a real line through zero with zero removed, or equivalently all nonzero <complex numbers> with the same <argument> modulo $\pi$.
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