Re: Sign and complex.

On 3/3/2025 3:16 PM, Chris M. Thomasson wrote:

On 3/3/2025 3:10 PM, Richard Hachel wrote:

Le 03/03/2025 à 23:38, "Chris M. Thomasson" a écrit :

On 3/3/2025 1:37 PM, Richard Hachel wrote:

Complex numbers and products of different complex signs.
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What is a complex number?
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It is initially an imaginary number which is a duality.
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The two real roots of a quadratic curve, for example, are a duality.
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If we find as a root x'=2 and x"=4 we can include these two roots in a single expression: Z=3(+/-)i.
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Z is this dual number which will split into x'=3+i and x"=3-i.
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As in Hachel i^x=-1 whatever x, we have: x'=2 and x"=4.
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Be careful with the signs (i=-1). If we add i, we subtract 1.
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If we subtract 5i, we add 5.
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But let's go further.
A small problem arises in the products of complexes.
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Certainly, if we take complexes of inverse spacings, that is to say (+ib) for one and (-ib) for the other, everything will go very well.
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Let's set z1=3-i and z2=4+2i.
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We have z1*z2=12+6i-4i-2i²=14+2i
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Let's set the inverse by permuting the signs of b:
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z1=3+i and z2=4-2i.
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We have z1*z2=12-6i+4i-2i²=14-2i
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We notice that each time, we did:
Z=(aa')-(bb)+i(ab'+a'b)
and that it works.
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Question: Why does this formula become incorrect for complexes of the same sign in b?
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Example Z=(3+i)(4+2i) or Z=(3-i)(4-2i)
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The formula given by mathematicians is incorrect.
I am not saying that it does not give a result.
I am saying that it is incorrect.

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Where would you plot say, 1+.5i on the plane? I would say at 2-ary point (1, .5), right where x = 1 and y = .5. Say draw a little filled circle at said coordinates in the 2-ary plane where:
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       (+y)
         ^
         |
         |
         |
(-x)<---0--->(+x)
         |
         |
         |
         v
       (-y)

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<http://nemoweb.net/jntp?myUYryqxSTftKUa3owdcVRxGpRA@jntp/Data.Media:1>
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R.H.

 So, you try to embed it all in the real line?

If so, it kinds of sounds akin to storing a 2d array inside of a 1d array? Is that somewhat similar?

So, why even have your y axis showing in your graphic? Show me a single point, color it yellow, on your real line that shows the plotted point 1+.5i.