Re: How? ? ?

On 4/2/2025 12:53 PM, Chris M. Thomasson wrote:

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?
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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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 sqrt(0+1i) has two roots:
 [0] = sqrt(0+1i)
[1] = -sqrt(0+1i)

Keep in mind that since this is only a sqrt the negation is akin to adding pi to the polar representation.

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