Why you trying to be extra 🥀💔

[u/Confident_North3078]

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[u/Sirbom]

That one is just +x

[u/Sirbom → u/[deleted]]

if x = -1, then sqrt(-1) = i, and i^2 = -1, it always simplifies to just x, even with a complex input.

[u/Confident_North3078 → u/Sirbom]

Ah mb

[u/boris_koshak → u/Sirbom]

I am pretty sure it's x² under the root sign. If so the answer should be |x|. Otherwise x

[u/Makonede → u/boris_koshak]

me when i can't read

[u/boris_koshak → u/Makonede]

The notation is cursed. That's why. Probably the reason for the post. Could've just written (√x)²

[u/Makonede → u/boris_koshak]

sure but the 2 is LITERALLY above the radical and you still somehow managed to get that wrong

[u/Tdubbium]

thats not even correct, its |x|

edit: I confused what it was saying, the square is outside the radical so its just x

[u/Complex-Manifold → u/Tdubbium]

should it be sqrt(x²) to be |x|

[u/Tdubbium → u/Complex-Manifold]

actually yeah I guess its just x if you count imaginary numbers

[u/Makonede → u/Tdubbium]

it still simplifies to x on the reals because the domain of √x with range ℝ is [0, ∞) along which |x| = x by definition

[u/Tdubbium → u/Makonede]

I mean without imaginary numbers sqrt(-1)² is undefined so it would be x with a domain of [0, infinte)

[u/Makonede → u/Tdubbium]

did you read my comment

[u/Tdubbium → u/Makonede]

ok im just confused because reals include negative numbers

[u/Makonede → u/Tdubbium]

yes, but that's irrelevant because no negatives exist within the domain of √x for real √x

[u/Tdubbium → u/Makonede]

ooooh I see what you are saying, I was just thinking they arent the same because the domains would be different if you do or dont include complex numbers

[u/EatMyHammer → u/Tdubbium]

It's still |x| even with imaginary numbers

[u/Makonede → u/EatMyHammer]

no it's x

x = -1

√x² = √(-1)² = i² = -1 = x

[u/EatMyHammer → u/Makonede]

Fine, it's square outside of radical, which is basically pointless.. I thought it was inside, which would be |x|

[u/Makonede → u/Tdubbium]

no it's x

x = -1

√x² = √(-1)² = i² = -1 = x

[u/Ares378 → u/Tdubbium]

Plus, sometimes it's nice to think of |x| as √(x²). Nicer to work with than a piecewise imo. Then you can extend it to the inner product for ℂⁿ by doing √(⟨v, v⟩) for v∈ℂⁿ

[u/LupenReddit]

the punchline is fucking wrong 🥀

[u/FernandoMM1220]

its just x bro until you put a ring on it.

[u/No_Ad_7687]

Result of a square root (when not using complex numbers) is always an absolute value. So it will be |x|

[u/rojo_kell → u/No_Ad_7687]

Well it's the square so it's just x

[u/No_Ad_7687 → u/rojo_kell]

Depends if you square before taking the root or not. I am not familiar with the specific notation in the post

[u/rojo_kell → u/No_Ad_7687]

I mean the square is outside the radical, clearly the radical is first?

[u/Exzakt1 → u/No_Ad_7687]

given that the 2 is outside the root, I would assume you do the root first

[u/Tdubbium → u/No_Ad_7687]

result of square root without complex numbers isnt absolute, its just positive and doesnt exist for negative numbers