Solution
= Solution
An <equivalence relation> is reflexive, symmetric, and transitive. Here
$$
|x-y|^2<|x|^2+|y|^2
\iff \operatorname{Re}(x\overline y)>0.
$$
The relation is reflexive and symmetric, but it is not transitive. For example, take
$$
x=1,\qquad y=e^{i\pi/3},\qquad z=e^{2i\pi/3}.
$$
The real parts of $x\overline y$ and $y\overline z$ are positive, whereas that of $x\overline z$ is negative. Hence this is not an equivalence relation.