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From: sobriquet <dohduhdah@yahoo.com>
Newsgroups: sci.math
Subject: Re: How? ? ?
Date: Wed, 2 Apr 2025 16:24:35 +0200
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Op 02/04/2025 om 15:14 schreef efji:
> Le 02/04/2025 à 15:05, Richard Hachel a écrit :
>> Le 02/04/2025 à 14:49, efji a écrit :
>>> 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
>>
>> Four possible values?
>>
>> To think that Python gave us a nervous breakdown when I explained that 
>> a function could have multiple roots, which was actually true.
>>
>> But here, we're falling into the opposite madness.
>>
>> We add two numbers, and we find four answers, which is stupid, to say 
>> the least.
> 
> We don't add two numbers since \sqrt{i} is not a number because this 
> notation is a nonsense ! Can you read carefully what I wrote ???

It seems to work just fine in wolfram alpha (desmos in complex mode 
gives the same answer).

https://www.wolframalpha.com/input?i=sqrt%28i%29

https://www.desmos.com/calculator/ztfet88jmu