Path: ...!news.mixmin.net!proxad.net!feeder1-2.proxad.net!usenet-fr.net!pasdenom.info!from-devjntp
Message-ID: <6bu9vkI1-cJwI0DVvl47MCKHzfQ@jntp>
JNTP-Route: nemoweb.net
JNTP-DataType: Article
Subject: Re: Division of two complex numbers
References: <zMjaMvWZUkHX6SOb195JTQnVpSA@jntp> <43067dc8-78c7-4053-848d-1eeff3688bbd@att.net>
Newsgroups: sci.math
JNTP-HashClient: 3GQu5W3r7Q3ctmsp5shvVRRfBJc
JNTP-ThreadID: EDRXv_p0dplN4woC0vmk_fQazIU
JNTP-Uri: https://www.nemoweb.net/?DataID=6bu9vkI1-cJwI0DVvl47MCKHzfQ@jntp
User-Agent: Nemo/1.0
JNTP-OriginServer: nemoweb.net
Date: Mon, 20 Jan 25 19:21:02 +0000
Organization: Nemoweb
JNTP-Browser: Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/131.0.0.0 Safari/537.36
Injection-Info: nemoweb.net; posting-host="e8cbf2474b472b9bb79db3dccb6a856bc1d05409"; logging-data="2025-01-20T19:21:02Z/9181252"; posting-account="4@nemoweb.net"; mail-complaints-to="julien.arlandis@gmail.com"
JNTP-ProtocolVersion: 0.21.1
JNTP-Server: PhpNemoServer/0.94.5
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
X-JNTP-JsonNewsGateway: 0.96
From: Richard Hachel <r.hachel@liscati.fr.invalid>
Bytes: 2029
Lines: 31

Le 20/01/2025 à 19:33, Jim Burns a écrit :
> On 1/20/2025 6:02 AM, Richard Hachel wrote:
> 
>> Division of two complex numbers.
>>
>> Now let's set Z=(a+ib)/(a'+ib')

> ((a + ib)(c + id))⃰  =
> (ac + i(ad+bc) + i²bd)⃰  =

No. You can't.

=(ac + i(ad+bc) + (ib*id)⃰  

You don't know what i is but at this moment, you know that it is both i=1 
and i=-1.
If it is 1 then 1²=1.
If it is -1 then -1²=1
In any case, its square will be 1 because in your two solutions, you will 
have to give your choice, but not both at the same time.

 

> (ac + i(ad+bc) + (sₑ+i⋅sₙ)bd)⃰  =
> ((ac+sₑbd) + i(ad+bc+sₙbd))⃰  =
> (ac+sₑbd) - i(ad+bc+sₙbd)

 ac+bd+i(ad+bc) with i=(+/-)1 at final choise.

R.H.