Re: Sign and complex.

On 3/3/2025 3:32 PM, Python wrote:

Le 04/03/2025 à 00:16, "Chris M. Thomasson" a écrit :

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.

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

 Don't try to make sense of Hachel's asinine products. There is none.

You know that forced me to laugh. One time, one of my mentors called me Chris (Plot Anything) Thomasson. In a good way. Well, sometimes I get a little bored, from time to time... ;^D