Can Complex Numbers Be Viewed as Real Numbers on the X and Y Plane?

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Discussion Overview

The discussion revolves around the interpretation of complex numbers as representations of two separate real numbers on the X and Y plane. Participants explore the implications of this representation and its consistency with fundamental mathematical principles.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how it is possible to ignore the addition sign and imaginary number in the context of complex numbers without contradicting fundamental mathematics.
  • Another participant asserts that nothing is ignored and challenges the correctness of a specific mathematical expression related to complex numbers.
  • A different viewpoint suggests that complex numbers can be viewed as two separate real numbers, emphasizing that the real and imaginary parts uniquely identify the complex number.
  • One participant draws an analogy with prime factorization in positive integers to illustrate the representation of complex numbers.
  • Several participants share links to external resources that discuss complexities and potential misunderstandings regarding complex numbers.
  • A participant acknowledges their difficulty in articulating their question but believes they have found the answer independently, indicating a level of personal resolution.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of complex numbers and their mathematical representation. There is no consensus on the fundamental questions raised, and the discussion remains unresolved.

Contextual Notes

Some statements rely on specific interpretations of mathematical expressions and definitions, which may not be universally accepted. The discussion includes unresolved questions about the nature of complex numbers and their representation.

Leo Authersh
How is it possible to ignore the addition sign and imaginary number without contradicting fundamental Mathematics?

I find it difficult to understand.
 
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Hi,
We don't ignore anything. Don't contradict anything either.
Leo Authersh said:
X2 + Y2 = (X + iY)/(X + iY)
is not correct. Where did you get this ?
 
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How can we consider a complex number as two separate real numbers for in X and Y plane?
It is just a different way to represent the numbers.
By giving the real and imaginary part of a complex number you can uniquely identify this number.

An analogy in the positive integers: You can write every number by its prime factorization.
You can write 2*3*5 or "2,3,5" instead of 30. Same thing, just written in a different way, and there is a 1:1 relation between numbers and their prime factorization.
 
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BvU said:
Hi,
We don't ignore anything. Don't contradict anything either.
is not correct. Where did you get this ?
True that. I have edited it. But my question is correct and after thinking about it, I have found the answer myself. I just find it hard to put into words the exact thing in my mind. That's why the question is incomprehensible. But I think fresh_42 has understood my question.

Thank you for the answer BvU :)
 
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