Re: How? ? ?

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.

Not really, see https://en.wikipedia.org/wiki/Principal_value#Square_root

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

The video is somewhat sloppy when it comes to distinguish properly branches of sqrt(x), anyway it ends up with the "right" result.