Path: ...!3.eu.feeder.erje.net!feeder.erje.net!proxad.net!feeder1-2.proxad.net!usenet-fr.net!pasdenom.info!from-devjntp Message-ID: JNTP-Route: nemoweb.net JNTP-DataType: Article Subject: Re: Equation complexe References: Newsgroups: sci.math JNTP-HashClient: zKASFOcchvfmuFJ0USKnhy5ZT0M JNTP-ThreadID: O5CXkAcAe1D7_dx2s1eq7KbScfI JNTP-ReferenceUserID: 4@nemoweb.net JNTP-Uri: https://www.nemoweb.net/?DataID=CBu8wFqdO3Grfl9vm8TrVYMDlas@jntp User-Agent: Nemo/1.0 JNTP-OriginServer: nemoweb.net Date: Tue, 25 Feb 25 20:38:27 +0000 Organization: Nemoweb JNTP-Browser: Mozilla/5.0 (Linux; Android 10; K) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/133.0.0.0 Mobile Safari/537.36 Injection-Info: nemoweb.net; posting-host="fd2131a9fa825445f413d5a0e5d54e5cdfeaa501"; logging-data="2025-02-25T20:38:27Z/9221963"; posting-account="190@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: Python Bytes: 2736 Lines: 41 Le 25/02/2025 à 21:07, Richard Hachel a écrit : > Le 25/02/2025 à 18:21, Jim Burns a écrit : >> On 2/25/2025 9:23 AM, Richard Hachel wrote: >> >>> x^4=-81 >>> >>> What is x? >> >> x ∈ {(+1+𝑖)⋅3/√2, (+1-𝑖)⋅3/√2, (-1+𝑖)⋅3/√2, >> (-1-𝑖)⋅3/√2} > > Oui, c'est ce que dis aussi l'Intelligence artificielle, mais sans trop > expliquer pourquoi. > > Personally, I propose only one root, but it is not in conformity with what is > said about "complex numbers". So it is not about complex as it is not only said but proven from the definition of complex numbers. > I remind you that I do not admit the definition i²=-1, It is not the definition, it is a consequence of a definition that I've shown you numerous times. You are a liar. > which, in itself, is not false, but so narrow that I do not understand its > semantic interest > For me, the definition must be extended to all powers of x such that i^x=-1. Which leads to immediate inconsistencies. This property is contradictory. > In short, it is necessary to go through a constancy of i^x=-1, like 1^x=1. > This defined, we easily have x^4=-81 if x=3i. > The other four roots being incorrect (in the proposed system). This is utter bullshit. As are all your your fantasies. Build on top of your ignorance, hypocrisies, stupidity and arrogance.