Path: ...!weretis.net!feeder9.news.weretis.net!news.quux.org!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: =?UTF-8?B?UmU6IHjCsis0eCs1PTA=?=
Date: Wed, 22 Jan 2025 14:57:28 -0800
Organization: A noiseless patient Spider
Lines: 29
Message-ID: <vmrt4o$18f0k$1@dont-email.me>
References: <4mVsl7f7IEYIck3oOw7iM3AOjN8@jntp> <vmrqo4$180ph$1@dont-email.me>
 <vmrs86$185g8$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 22 Jan 2025 23:57:29 +0100 (CET)
Injection-Info: dont-email.me; posting-host="464af39ea2d015cab4edf118f2c36543";
	logging-data="1326100"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+ZI6sPZp1F+k+20SsQ7aHVgRmQ0l8zteY="
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:nIWdcU5oJvholK9gkJWRZkygN18=
Content-Language: en-US
In-Reply-To: <vmrs86$185g8$1@dont-email.me>
Bytes: 2009

On 1/22/2025 2:42 PM, Moebius wrote:
> Am 22.01.2025 um 23:16 schrieb Chris M. Thomasson:
>> On 1/22/2025 5:48 AM, Richard Hachel wrote:
> 
>>> x² + 4x + 5 = 0
>>>
>>> This equation has no root, and <bla>
> 
> It has the two "roots" (solutions):
> 
> x = -2 - i
> x = -2 + i
> 
> Hint:
> 
> x² + 4x + 5 = (x + 2)² + 1.
> 
> Hence x² + 4x + 5 = 0 is equivalent with (x + 2)² + 1 = 0 or (x + 2)² = 
> -1. So x + 2 has to be a (one or more) complex number(s) z such that z² 
> = -1. We know such numbers, they are i and -i (and there aren't more). 
> Hence we have x + 2 = i or x + 2 = -i resp. And hence x = -2 + i or x = 
> -2 - i resp.
> 
>> The x^2 component has two roots.
> 
> Doesn't make much sense. :-P

Shit happens. When I see x^2 and think of complex numbers, I think of 
two roots. This can imply that there are two solutions.