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501 Glorious LeaderAbout michel123456

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 Birthday 06/08/1960
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Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
It is negative. And I guess all these points are upon an hyperbola. But I don't know if that can have a deeper signification. That was not my goal. 
Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
This one, both axes If they are labelled i on both axes we have Point A has coordinates 6i, 9i The area of the green rectangle is 6i.9i=54i^2=54 It has area the number 54, that you can also put on the number line at position 54. 
Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
Could you please label your axis? I don't follow. 
What are you listening to right now?
michel123456 replied to heathenwilliamduke's topic in The Lounge

Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
I guess it represents the number 54. As if the area were representing a distance upon the number line. 
Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
I understand that the surface of my "i diagram" is spread with real numbers. That the blue square is a "real square" of imaginary side. And so is the red square. And that those squares are not representing areas but maybe a weird unauthorized representation. All of which make the imaginary numbers totally different from the real numbers. Which again makes me wonder how can you consider correct to create a representation with an axis of imaginary numbers orthogonal to an axis of real numbers just as if they were of equivalent nature. https://en.wikipedia.org/wiki/Imaginary_number#/media/File:Complex_conjugate_picture.svg In this diagram, how do we infer that iy has a positive value? How do we treat the imaginary line on the same ground with the real number line? Where are the positive & negative? I mean, one would automatically infer that the positive numbers are on the upper right sector. Is it so? And why? 
Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
I'll try to explain. I have those 2 graphs: If I try to superpose the one with the other, even in 3D space, they do not fit together. There is nothing common in those 2 graphs that would offer the possibility to put one perpendicular to the other. The only common ground is the point zero. All the rest is pure contradiction. IOW I don't understand how one can put the i axis perpendicular to the Real number axis. The meaning of the product gets ambivalent: does 3i follow the rule of the Real numbers (3i is positive) or does it follow the rule of i (3i is negative)? 
Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
Yes, I see the difference now. Thank you for the clarification. That is part of my question. The multiplication rule for i looks to me completely incompatible with the multiplication rule of the Real numbers. As shown in my graph. 4. There is no common ground. 
Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
Well understood. I got confused by https://www.wolframalpha.com/input/?i=i^2 And https://www.google.com/search?q=i^2&oq=i^2&aqs=chrome..69i57j69i64.5694j0j7&sourceid=chrome&ie=UTF8 Why? You can invent it. What is wrong with this concept? 
Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
Thank you. That is not what I get from a search, even not in Wolfram Alpha. 
Elucubrations on positve, negative & imaginary numbers
michel123456 replied to michel123456's topic in Speculations
I have combined 2 imaginary axis. The same way as I have combined 2 Real number axis previously. It is a different approach than combining Real & Imaginary as perpendicular. 
At the risk of being completely idiot here below something I wonder: Step1: the positive & negative on the number line. This above is a representation of the number line, the Real numbers going from zero to positives on the right & negative to the left. Step 2: When it comes to multiplication, we can show the sign rule in the following diagram. Where we have the product of 2 positives is positive. The product of a positive with a negative is a negative, the product of 2 negatives is a positive. Step 3: From the diagram above it comes out that the square of a Real number, positive or negative, is always positive. As shown below, the 2 squares are in a positive area. Step 4: Then we go to imaginary numbers (Complex numbers), in such a way that negative squares can be handled, as shown below. Where we see that i^2=1 (the blue square). Question 1 is: where is the catch? Why is this diagram wrong? Why i^2 (the red square) shows negative in the diagram? Although the correct answer is that i^2=1 Question 2 is the following: what is the sign of 2i? Is it positive or negative? Do we follow the rule of the Real numbers, or the rule of Imaginary numbers? Question 3 is: how can you combine the Real number diagram with the Imaginary number diagram? Where is the common axis? The only common feature is a point: zero.

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