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→Unique square root of -1 necessary for complex analysis
:::::::::: That's unnecessary semantics. Replace "rigorous" with whatever substitute you prefer, but a proof that relies on fewer or less doubtful assumptions is more [rigorous/robust/credible/advantageous] than one that relies on many or more doubtful assumptions. For example, a proof that relies on the [[Axiom of Choice]] is not as good as one that solves the same problem without resorting to that axiom.--[[User:Aschlafly|Andy Schlafly]] 11:19, 10 April 2012 (EDT)
:::::::::: That's unnecessary semantics. Replace "rigorous" with whatever substitute you prefer, but a proof that relies on fewer or less doubtful assumptions is more [rigorous/robust/credible/advantageous] than one that relies on many or more doubtful assumptions. For example, a proof that relies on the [[Axiom of Choice]] is not as good as one that solves the same problem without resorting to that axiom.--[[User:Aschlafly|Andy Schlafly]] 11:19, 10 April 2012 (EDT)
:::::::::::How about intuitive? That seems to be the main concern here, that imaginary numbers are not something we can easily wrap our heads around. [[User:JustinD|JustinD]] 15:23, 10 April 2012 (EDT)
Slightly off-topic, but you might be interested in physical evidence for complex numbers. According to this new paper [http://arxiv.org/abs/1204.1858], imaginary numbers are the most crucial difference between classical and quantum mechanics. [[User:RSchlafly|RSchlafly]] 20:50, 9 April 2012 (EDT)
Slightly off-topic, but you might be interested in physical evidence for complex numbers. According to this new paper [http://arxiv.org/abs/1204.1858], imaginary numbers are the most crucial difference between classical and quantum mechanics. [[User:RSchlafly|RSchlafly]] 20:50, 9 April 2012 (EDT)