Rafael Bombelli & Imaginary Numbers: The Pros & Cons

In summary: So, the summary is: In summary, imaginary numbers were first thought to be useless by Rafael Bombelli, but other disciplines, notably physics, have found a use for them. Despite their unfortunate name, imaginary numbers have real and practical uses and are no longer being campaigned against.
  • #1
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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  • #2
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.
 
  • #3
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.
 

Related to Rafael Bombelli & Imaginary Numbers: The Pros & Cons

1. What are imaginary numbers and why are they important?

Imaginary numbers are numbers that can be written in the form of a real number multiplied by the imaginary unit, i, which is equal to the square root of -1. These numbers are important because they allow us to solve equations that would otherwise have no real solutions, and they have many applications in mathematics, physics, and engineering.

2. Who is Rafael Bombelli and what is his contribution to the understanding of imaginary numbers?

Rafael Bombelli was an Italian mathematician who lived in the 16th century. He is best known for his work on complex numbers and for introducing the concept of using i as an imaginary number. Bombelli's work helped to pave the way for the development of the complex number system and the understanding of imaginary numbers.

3. How are imaginary numbers used in real-world applications?

Imaginary numbers are used in a variety of real-world applications, such as in electrical engineering, quantum mechanics, and signal processing. They are also used in the study of periodic functions, such as sound waves and electromagnetic waves. In addition, imaginary numbers are used in the solution of differential equations, which have many practical applications in physics and engineering.

4. What are the pros and cons of using imaginary numbers?

The main pro of using imaginary numbers is that they allow us to solve equations that would otherwise have no real solutions. They also have many practical applications in various fields of science and engineering. However, one of the cons of using imaginary numbers is that they can be difficult to understand and may seem abstract to some people. Additionally, the use of imaginary numbers can sometimes lead to erroneous results if not used correctly.

5. How can one visualize or represent imaginary numbers?

One way to visualize imaginary numbers is by representing them on a complex plane, where the real numbers are shown on the horizontal axis and the imaginary numbers on the vertical axis. This allows us to graph and perform operations on complex numbers, making it easier to understand and work with them. Imaginary numbers can also be represented geometrically as points in a two-dimensional plane or as vectors with a magnitude and direction.

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