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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: =?UTF-8?B?UmU6IHjCsis0eCs1PTA=?=
Date: Wed, 22 Jan 2025 15:02:35 -0800
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On 1/22/2025 2:57 PM, Chris M. Thomasson wrote:
> 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.

For instance, this should have three roots?

x^3+1+x^2 = 0

What am I missing here? Sorry if it's something obvious.

Shit.