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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How? ? ?
Date: Wed, 2 Apr 2025 12:53:32 -0700
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On 4/2/2025 5:49 AM, efji wrote:
> Le 02/04/2025 à 14:32, Richard Hachel a écrit :
>> How can mathematicians come up with such absurdities?
>>
>> https://www.youtube.com/watch?v=XZriBHTNPw0
>>
> 
> No mathematician would write \sqrt{i} because the symbol "\sqrt" designs 
> the positive square root of a real number, which does not make sense in 
> \C since it is not an ordered set and the word "positive" is a nonsense 
> in \C.
> 
> Anyway, "i" has 2 square roots : ±(1+i)/\sqrt{2}
> and "-i" too : ±(1-i)/\sqrt{2}
> Thus, the mathematically wrong expression "\sqrt{i}+\sqrt{-i}" is non 
> univoque and could be any of these 4 values :
> 
> ±\sqrt{2}, ±i\sqrt{2}
> 
> You're welcome
> 

sqrt(0+1i) has two roots:

[0] = sqrt(0+1i)
[1] = -sqrt(0+1i)

any of them raised to the the 2'nd power equals 0+1i.