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> When people say they don't "get" complex numbers, usually they mean they've seen them mentioned, but have never actually done anything with them.

What people complain about is that they do not have a (real or hypothetical) device which can display its measurements as a complex number while they do have devices which measure properties in terms of integer, rational and real numbers.

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Real numbers almost certainly are just as fictional as complex numbers. Physics doesn't seem to admit infinitely precise measurements, so literally no theoretical device can operate with real numbers.

Even if real numbers are "real", only a countable number of them are computable, even in theory. The rest are probably completely inaccessible, barring hypercomputation. (Interestingly, access to true real numbers gives you hypercomputation as a side-effect)

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