this post was submitted on 16 Sep 2024
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[–] [email protected] 95 points 4 months ago (2 children)

Well actually it’s the other way around. The reason imaginary numbers were invented was to solve a problem we’d been crying over for centuries.

Then, as in most cases, solving one problem opens the door to millions of other problems like why in the fuck does the universe use these imaginary numbers we made up to solve cube roots?

Why is i a core part of the unit circle with like e^i*pi^ ? “Oh that’s because i is just perpendicular to the real number line” ?! Say that sentence again, how the fuck did we go from throwing sharp sticks to utterly deranged sentences like that? More importantly why do utterly deranged sentences like that accurately describe our universe and what is the next ludicrous math concept we’re going to discover is integral to the function of the universe?

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[–] [email protected] 18 points 4 months ago (2 children)

https://lemmy.blahaj.zone/post/15648655

I wrote a piece about why imaginary numbers are actually important. It's in german though.

To sum it up, to every polynomial equation, there exists at least one solution to it, if you allow complex numbers to be solutions.

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[–] [email protected] 36 points 4 months ago (8 children)

Hate to break it to you, but all numbers are imaginary.

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[–] [email protected] 12 points 4 months ago (2 children)

Is that number with us in this room right now?

[–] [email protected] 1 points 4 months ago* (last edited 4 months ago)
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[–] [email protected] 78 points 4 months ago* (last edited 4 months ago) (4 children)

Imaginary is a poor name for them because it implies they dont exist. Complex numbers[/component] is more appropriate

[–] [email protected] 0 points 4 months ago (1 children)

Well it's true, they don't exist

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[–] [email protected] 5 points 4 months ago (1 children)

The Italian Bombelli in 1572 seemed to toy with both concepts but called imaginary numbers “quantità silvestri” (silvestri meaning ‘wild’) and complex numbers “numeri complessi”. Interesting the imaginary is a quantity and the complex is a number, but maybe old Italian didn’t have that distinction.

I suppose Descartes would agree with you, he first coined the term “imaginary” because he didn’t think they’d serve much purpose. Euler made use of them and continued using the term. Complex number is a complex - a number with a real and an imaginary component.

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[–] [email protected] 36 points 4 months ago (1 children)

Complex numbers ≠ Imaginary numbers

[–] [email protected] 27 points 4 months ago (1 children)

Imaginary numbers are any number multiplied by the square root of negative 1, a complex number has both a real and imaginary part. 10+i is complex, 10*i is imaginary.

[–] [email protected] 21 points 4 months ago* (last edited 4 months ago)

Yep. So my point still stands. Imaginary numbers are a part of complex numbers

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[–] [email protected] 39 points 4 months ago (6 children)

Fine, then you figure out what the square root of a negative number actually is!

[–] [email protected] 12 points 4 months ago (3 children)

My calculator says they are an "error".

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