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[carey]

(12-09-2024 11:44 PM)dm319 Wrote:  I'm probably more a complex-number-denier but I think I'm starting to come round.

What did it for me in the debate whether complex numbers are a necessity or a mathematical convenience occurred in high school when my chemistry teacher introduced the Schrödinger equation (thank you Mr. Cardulla!) and there it was, i, in the equation itself, suggesting a fundamental role of complex numbers in nature. That didn't stop diehard deniers of the necessity of complex numbers from pointing out that "complex numbers are just ordered pairs of real numbers." However the argument that complex numbers can be expressed using real numbers behaving like complex numbers doesn't appear to me to undercut the necessary role of the complex number structure.