Why Did People Accept Imaginary Numbers Before Negative Numbers?

[thejinx0r]

Hey Guys,

I am looking for a book that talks about the history of imaginary numbers and how people came to need it.

I'm just having trouble imagining how people could have accepted imaginary numbers before negative numbers (at least in the western world).

Thank you,
Eric

P.S.
If there's a book that reads like a novel, it would be better :)

 

[arildno]

Imaginary numbers first appeared on the stage in the 16th century, as quantities that could formally be manipulated when solving cubic equations.

I have looked a bit about, the following book be Paul Nahin: "An imaginary tale" seems to be something you might trry out 8haven't read it myself).
A warning, however:
Quite a few of the negative reviews at amazon.com says it is "too heavy" on the maths, I hope that won't scare you away.
https://www.amazon.com/dp/0691127980/?tag=pfamazon01-20

 

[Hurkyl]

I'm just having trouble imagining how people could have accepted imaginary numbers before negative numbers (at least in the western world).

I thought that both began to 'widespread' acceptance at the same time -- with the method solution to cubic equations.

 

[thejinx0r]

Imaginary numbers first appeared on the stage in the 16th century, as quantities that could formally be manipulated when solving cubic equations.

I have looked a bit about, the following book be Paul Nahin: "An imaginary tale" seems to be something you might trry out 8haven't read it myself).
A warning, however:
Quite a few of the negative reviews at amazon.com says it is "too heavy" on the maths, I hope that won't scare you away.
https://www.amazon.com/dp/0691127980/?tag=pfamazon01-20

Cool, will check it out.

I just hate how they called it imaginary and how people truly believe that you cannot "imaginary" numbers in forced damped oscillators

:S

I thought that both began to 'widespread' acceptance at the same time -- with the method solution to cubic equations.

True, but from what I recall, for the quadratic, they always rewrote the equations such that there were only positive terms in there. So there were 4 different equations for solving the quadratic.

Then when they realized that imaginary numbers had a negative inside, they found it easier to accept that a negative because there were no way of having the sqrt of a positive number equal to i.

But anyways, I'm just studying for my Algebra class now and was thinking about it when I was doing quotient rings.

So there must have been another period in time where imaginary numbers were developed independently of solving the cubic equation, although I am in the part that says "every polynomial has a root in a bigger field". So maybe that was the only time where imaginary first came up.

 

[Hurkyl]

I just hate how they called it imaginary

We have Gauss to think for pushing the term "complex number", in his efforts to avoid this connotation. Alas, he was unsuccessful with his attempt to push the term "lateral part" as a replacement for "imaginary part".

So there must have been another period in time where imaginary numbers were developed independently of solving the cubic equation

I know negative numbers have been around since antiquity. I'm pretty sure the beginnings of the idea of complex number had been around a long time too; I have vague recollections of people playing with ways to represent solutions of quadratic equations that didn't have real roots; something with circles, I think. (The center worked out to being the real part, and radius to the imaginary part, I think)