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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Sign and complex.
Date: Mon, 3 Mar 2025 15:19:33 -0800
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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.
>>>>
>>>> What is a complex number?
>>>>
>>>> It is initially an imaginary number which is a duality.
>>>>
>>>> The two real roots of a quadratic curve, for example, are a duality.
>>>>
>>>> If we find as a root x'=2 and x"=4 we can include these two roots in 
>>>> a single expression: Z=3(+/-)i.
>>>>
>>>> Z is this dual number which will split into x'=3+i and x"=3-i.
>>>>
>>>> As in Hachel i^x=-1 whatever x, we have: x'=2 and x"=4.
>>>>
>>>> Be careful with the signs (i=-1). If we add i, we subtract 1.
>>>>
>>>> If we subtract 5i, we add 5.
>>>>
>>>> But let's go further.
>>>> A small problem arises in the products of complexes.
>>>>
>>>> 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.
>>>>
>>>> Let's set z1=3-i and z2=4+2i.
>>>>
>>>> We have z1*z2=12+6i-4i-2i²=14+2i
>>>>
>>>> Let's set the inverse by permuting the signs of b:
>>>>
>>>> z1=3+i and z2=4-2i.
>>>>
>>>> We have z1*z2=12-6i+4i-2i²=14-2i
>>>>
>>>> We notice that each time, we did:
>>>> Z=(aa')-(bb)+i(ab'+a'b)
>>>> and that it works.
>>>>
>>>> Question: Why does this formula become incorrect for complexes of 
>>>> the same sign in b?
>>>>
>>>> Example Z=(3+i)(4+2i) or Z=(3-i)(4-2i)
>>>>
>>>> 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.
>>>
>>> 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:
>>>
>>>        (+y)
>>>          ^
>>>          |
>>>          |
>>>          |
>>> (-x)<---0--->(+x)
>>>          |
>>>          |
>>>          |
>>>          v
>>>        (-y)
>>
>> <http://nemoweb.net/jntp?myUYryqxSTftKUa3owdcVRxGpRA@jntp/Data.Media:1>
>>
>> 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.