A link from complex number to hypercomplex numbers

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Discussion Overview

The discussion revolves around the relationship between complex numbers and hypercomplex numbers, specifically exploring whether there are problems that necessitate the introduction of hypercomplex numbers in a manner analogous to how complex numbers were introduced to solve certain real number problems.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that complex numbers arose from the need to solve real number problems that lacked real solutions, particularly in relation to square roots of negative numbers.
  • The same participant questions whether there exists a problem that uses complex numbers but lacks a solution in that domain, thus requiring hypercomplex numbers.
  • Another participant directs attention to external resources, implying that further exploration of quaternions or hypercomplex numbers may provide insight.
  • A third participant shares a link to a resource that may address the inquiry regarding number sets beyond complex numbers.
  • A later reply expresses gratitude for the information shared, indicating it was helpful in addressing their question.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus, as participants explore different aspects of the relationship between complex and hypercomplex numbers without resolving the initial question posed.

Contextual Notes

Participants do not clarify specific assumptions or definitions regarding hypercomplex numbers, nor do they resolve the mathematical implications of their discussion.

Den Webi
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If i understand correctly, the discovery of complex numbers was linked to solving real number problems, s.a. finding square roots of negative numbers. In other words, at first there was a problem that was formulated using real numbers only that had no real number solutions, which lead to extending the concept of numbers to include complex numbers.

Is there a similar problem that uses complex numbers only but has no complex number solution and requires the introduction of hypercomplex numbers?

Or is it that hypercomplex numbers were discovered/invented by simply adding extra dimensions to complex numbers?

Thank you in advance!
 
Mathematics news on Phys.org
Khashishi, thank you so much, that's exactly what i was looking for!
 

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