# How old is i? (Imaginary number)

#### Tyrion101

A couple of things I've read or heard in class suggest it's been around for a very long time. I got the impression it's from antiquity, but am I wrong?

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#### Tyrion101

Interesting, any idea how right this is?

#### Mark44

Mentor
Interesting, any idea how right this is?
How right what is? Do you have a specific question about the wiki article?

#### Tyrion101

Well wiki can be really wrong at times, and I was wondering if anything seemed amiss.

#### Mark44

Mentor
Well wiki can be really wrong at times, and I was wondering if anything seemed amiss.
It's a pretty short article -- I don't see anything that jumps out at me as being wrong.

#### epenguin

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Gold Member
It's an oft told tale, the idea was come across by Italian mathematicians Tartaglia, Cardano, Bombelli (who actually did what is a complicated story) in the Renaissance, in the 16th century. Arguably the most important peice of math ever done, no one will dispute one of the most.

Complex numbers can now be given a concrete image you probably know and made fairly obvious. Used by engineers and practical people every day. But that was only thought of centuries later. At the time it was just the square root of minus one which "obviously can't exist" but suspending disbelief if it existed they could use it in calculations (namely for solving cubic equations) and get just real number results, it worked! They called it strange names like "less of minus" or something. I think that was the first time they ever worked with such a thing of which there was no concrete model, that makes it quite pathbreaking, and set a new pattern for math, which is why it is so important.

They didn't like having to do it, and for a long time they thought it was a temporary expedient or shortcut, till they could find a more satisfactory way of solving cubics etc. I read it has been proved There Is No Alternative, that hey cannot be avoided in solving cubics and other problems - I don't know how advanced that proof is.

I am writing this from memory but there are loads of books on this history.

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#### DaveC426913

Gold Member
There is a book-length treatment of the number i called An Imaginary Tale, which can be found on Amazon:
Emboughtened. Thank you.

#### Tyrion101

It's an oft told tale, the idea was come across by Italian mathematicians Tartaglia, Cardano, Bombelli (who actually did what is a complicated story) in the Renaissance, in the 16th century. Arguably the most important peice of math ever done, no one will dispute one of the most.

Complex numbers can now be given a concrete image you probably know and made fairly obvious. Used by engineers and practical people every day. But that was only thought of centuries later. At the time it was just the square root of minus one which "obviously can't exist" but suspending disbelief if it existed they could use it in calculations (namely for solving cubic equations) and get just real number results, it worked! They called it strange names like "less of minus" or something. I think that was the first time they ever worked with such a thing of which there was no concrete model, that makes it quite pathbreaking, and set a new pattern for math, which is why it is so important.

They didn't like having to do it, and for a long time they thought it was a temporary expedient or shortcut, till they could find a more satisfactory way of solving cubics etc. I read it has been proved There Is No Alternative, that hey cannot be avoided in solving cubics and other problems - I don't know how advanced that proof is.

I am writing this from memory but there are loads of books on this history.
I may actually read it it sounds fascinating.

#### epenguin

Homework Helper
Gold Member
Bombelli's father was hanged in the public square in Bologna (for political, not criminal, offences). Not a lot of people know that.
I met the man discovered that in the archives. It's now in a book I have somewhere - but that is getting as hard to find as it was in the original archives.

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