Quaternions and the ather hypercomplexe numbers

[matteo16]

apologie me if this question isn't corret or is simple for you

do solutions of an equation as quaternions or as the ather hypercomplex numbers exist?

wath do they do in physics?

for exemple ottonions or sedenions

do ather hypercomplex numbers exist?

 

[matt grime]

Yes, of course there are solutions in quaternions to things like x^2+1=0 (there are many, in fact, that being the whole point) and of course the real numbers are a subset of the quaternions...

As for physics, look at John Baez's website (google for it).

 

[tacman]

Quaternions and other hypercomplex numbers are a fascinating topic in mathematics that have many applications in physics. To answer your first question, yes, solutions of equations can exist in the form of quaternions or other hypercomplex numbers. In fact, these numbers were originally developed as a way to extend the concept of complex numbers and provide solutions to certain types of equations that could not be solved using real or complex numbers alone.

In physics, quaternions and other hypercomplex numbers have been used in a variety of ways. One example is in quantum mechanics, where they have been used to describe the spin of particles. They have also been used in electromagnetic theory to describe rotations and transformations in three-dimensional space. In general, these numbers have been found to be useful in describing and solving problems involving rotations, transformations, and symmetries in physics.

As for other hypercomplex numbers such as octonions or sedenions, they do indeed exist and have been studied extensively in mathematics and physics. These numbers have even more complex properties than quaternions, and their applications in physics are still being explored. Some theories, such as the M-theory in string theory, use these higher-dimensional hypercomplex numbers to describe the fundamental forces of nature.

In summary, quaternions and other hypercomplex numbers have a wide range of applications in physics and continue to be an active area of research. So, there is no need to apologize for asking about them, as they are a complex and interesting topic that even experts in the field are still studying and learning about.