Complex numbers can be ordered, and Numpy uses the lexicographic order. It's true that no ordering exists that satisfies similar relations vs. both addition and multiplication as for reals. But I don't think the present behavior is really incorrect. One an argue that it is inconsistent both with Python, though, and I suspect there's not that much code that correctly makes use of this.

There was some discussion previously and we were seriously considering deprecating it in gh-15981, and not long ago Rakesh started working on that in gh-17030.

That said, it is hard to say what fallout might crop up which may lead us to keep the current behaviour. And it indeed is not a bug as such.

I am going to close this in favor of the linked issue, @nschloe if you want to discuss this further, I would suggest commenting either on the issue or PR.