Rafael Bombelli & Imaginary Numbers: The Pros & Cons

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Rafael Bombelli introduced imaginary numbers, initially deemed useless, but their application has expanded significantly, particularly in physics. Critics question their legitimacy, using analogies like failing to fill a room to illustrate perceived absurdities. Supporters argue that imaginary numbers have practical and real-world applications, such as simplifying complex calculations in physics. The debate highlights a divide between traditional mathematical views and modern applications in scientific fields. Overall, the utility of imaginary numbers in mathematics and physics is widely recognized despite initial skepticism.
muser
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Rafael Bombelli first used them and at the time they were thought to be useless. with other discplines (notably physics) finding a use for 'imaginary' numbers, why wasn't it's use curtailed? afterall if I was paid to fill a room with a 1000 people and could only manage 500. would i be within my rights to tell my employer when they ask, that the 500 missing guests, are imaginary. In my mind the whole SUSY theory is tainted by this crude use of mathemathics. are proponents for and against this stance?
 
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muser said:
Rafael Bombelli first used them and at the time they were thought to be useless. with other discplines (notably physics) finding a use for 'imaginary' numbers, why wasn't it's use curtailed? afterall if I was paid to fill a room with a 1000 people and could only manage 500. would i be within my rights to tell my employer when they ask, that the 500 missing guests, are imaginary. In my mind the whole SUSY theory is tainted by this crude use of mathemathics. are proponents for and against this stance?
:rolleyes: Sounds like you need to learn what imaginary numbers are and how they are used. Your example makes no sense. Despite their unfortunate name, imaginary numbers have very real and practical uses in describing the world. The day for campaigning against those crazy "imaginary" numbers is long gone.
 
You would appreciate imaginary numbers if you saw the calculation savings that result from considering a sinusoid to be the projection of the tip of a vector rotating in the real-imaginary plane.

You should enjoy them for many reasons, but this is one notable practical example.
 

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