How do you pronounce "over the complexes"?
Is there an agreed-upon way to say "complexes" in the sense of "the set of complex numbers" (as in "solve over the complexes")? Do we keep the stress on the first syllable (as in "complexes of buildings") or do we shift it to the second one (as in "complexity" or "non-complex")?
As a math major as an undergraduate who studied complex analysis, among other subjects (i.e. the calculus of complex numbers), the pronunciation we used (in an Ohio liberal arts college and an Ohio public university in the late 1980s amd 1990s) was to keep the stress on the first syllable (as in "complexes of buildings") and was not to shift it to the second one (as in "complexity" or "non-complex").
Given the diverse educational and regional backgrounds of my professors and the unanimity of the pronunciation, I believe that this is a fairly reliable indicator of the American English norm.
The term when referring to the set of all complex numbers should be plural (i.e. complexes, not complex) because the concept is inherently plural (akin to the reals, the rationals, the irrationals, etc.) and is generally given a plural character grammatically. (For what it is worth, mathematicians are, in my experience, also more likely to treat the word "data" as a plural rather than singular word, than non-mathematicians.)
This said, lots of people who would talk in public about the complexes are introverts who grew up mispronouncing many words that they learned through book reading, and are not infrequently non-native English speakers, so there would be tolerance of alternative pronunciations in most cases.
If you don't want to rely merely on the SE, I would recommend watching educational YouTube videos where this topic would come up, or online video of mathematics and theoretical physics conferences where the term would be used (e.g. twistor theory in physics), which is vastly more widely available than it was even pre-pandemic, since almost all major academic conferences in the past two years have been held in an online format.