ABSTRACT
A few years ago, in a conversation with a mathematician, I complained about my students' resistance to the seemingly simple idea of a complex number. The mathematician would not accept the claim that the subject might be inherently diffIcult. He hinted that it could be a problem of an incompetent teacher rather than of incapable students or a diffIcult subject matter. I insisted that there is a stumbling block, the nature of which was not yet clear to me. I brought lots of evidence. Eventually, the mathematician seemed to be giving up. 'Yes, the problem might be somewhat more complex than I thought', he said. But then, after a thoughtful pause, he exclaimed: 'Ok, it's diffICult, but I assure you that I would make the students understand the idea in no time: I'd just write the axioms of a complex field and show that the concept is well-defIned.'
