Re: How? ? ?

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?
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https://www.youtube.com/watch?v=XZriBHTNPw0
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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.
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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 :
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±\sqrt{2}, ±i\sqrt{2}
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You're welcome

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Four possible values?
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To think that Python gave us a nervous breakdown when I explained that a function could have multiple roots, which was actually true.
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But here, we're falling into the opposite madness.
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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