Rafael Bombelli & Imaginary Numbers: The Pros & Cons

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SUMMARY

Rafael Bombelli first introduced imaginary numbers, which were initially dismissed as useless. However, their application in various fields, particularly physics, has proven their value. Critics argue that the use of imaginary numbers can lead to misconceptions, as illustrated by the analogy of filling a room with guests. Proponents highlight the practical benefits of imaginary numbers, such as simplifying calculations involving sinusoidal functions through vector projections in the complex plane.

PREREQUISITES
  • Understanding of complex numbers and their properties
  • Familiarity with mathematical concepts in physics
  • Knowledge of vector projections in the complex plane
  • Basic grasp of sinusoidal functions and their applications
NEXT STEPS
  • Research the applications of imaginary numbers in electrical engineering
  • Learn about complex analysis and its relevance in physics
  • Explore the role of imaginary numbers in quantum mechanics
  • Study vector calculus and its connection to sinusoidal functions
USEFUL FOR

Mathematicians, physicists, engineers, and students interested in the practical applications of imaginary numbers and their significance in various scientific fields.

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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