What IS an imaginary number and and how is it used ?

What IS an imaginary number and and how is it used ?
an imaginary number is what you get when you find the square root of a negative number. for example, the square root of 1 is imaginary and is represented by "1i" The i is equivalent to "the square root of negative one". So the square root of 25 is 5i.
Erm.........I have just tried to input 5 and find out the square root of it using a calculator.....although I get an error. (Invalid input for function)
Any ideas ?
That's because your calculator (ie the bill gates sold you)  is crap  you'll need a scientific/engineering calculator which allows mathematics on imaginary numbers. It's usually marked r>p or p>r (polar rectangular coordinates).
Your calculator can only give one answer to a sum, there are two roots though to any number ie 16=+/ 4^2.
Your calculator lives in 'line land'  you need to get one that works in 'plane land' :wink:
no scientific calculator i've ever seen works on imaginary numbers.
however the $200 (Australian Dollar) graphics calculator, which i hired out through my school and thus was saved from having to pay that rediculous amount of money, does the job reasonably well.
but you can do calculations just fine with pen and paper.
A few sharp calculators do  the one i had in undergrad could handle complex arithmetic and some basic matrix algebra.
Complex numbers are important as they are algebraic completion of the reals  or translated into normal language any polynomial with real coefficients has a complex zero.
The actual construction of the numbers aint too difficult  but lets leave that for another post.
Here is an easy example, consider the polynomial f(x) = x<sup>2</sup> + 1 which obviously does not have a real zero. The complex number i is defined to be that number such that f(i) = i<sup>2</sup> + 1 = 0. Now there is nothing too amazing there, the real interesting thing is that you only have to add extend the reals once to make them algebraicly complete!
The three Scientific Calcs I have are the Casio FX7000G, Casio FX590, and FX992vb  all have it RP functions,  the 590 is getting on for 20 years old now.
I think i had the Sharp EL506WB (or what ever its predecessor was, i cant remember now)  was quite a handy little beast
the TI83(+) and i'm sure TI84 can handle imaginaries. That's what's the standard issue is in my school.
CASIO fx82MS is pretty substandard then, don't know how old that is. thats standard issue in my school. the other scientific calculators i've seen must have been horribly old.Originally Posted by Megabrain
we get issued with TI84's if we need them, but i hardly ever used mine for dealing with complex numbers.
Yes. to be honest im complete rubbish at maths. the most advanced mathematics i know would be very basic algebra. i.e x + 7 = 10 therefore x = 3.
Thats it.
Oh and the equivalent sign  i learned that just a month ago. still dont know how to use it though.
I do have a particular dislike for mathematics though i guess its because i hate rounding up / rounding down numbers. the laws of nature dont subscribe to mathematics and therefore do not necessarily come in integers.
I found me old calculator  was the Sharp EL506V
If i want a programmable calculator i would get the HP12C, if i wanted a graphics calculator i would get a laptop with matlab and mathematica installed on it lol.
Err... Very little in math deals with integers. For example, if x + 7.35 = 10.12, then x = 2.77. Also, number such as pi and e can't be expressed in any finite number of integer values. (Unlike 2.77 which equals 277/100.) Also, most modern research in physics (that I know of at least) says that the universe is quantized, meaning that in fact the laws of nature do come in integers.Originally Posted by leohopkins
Math is the exact opposite for me since through it a lot of nature can be understood. It was math alone through Dirac that showed a positron may exist even when that wasnt even the expected result. Just fell out of the equation as one of the answers. It was shown they existed a few years later by Carl Anderson.
Yeah, that's the schoolbook definition. I don't like it, and I'll tell you why.Originally Posted by Chemboy
Suppose we define √1 = i. We know that, in general, for positive real x, there are two solutions to √x  positive and negative, e.g. √4 = ±2. To be consistent, then, we would have to admit that √1 = ±i, either that or to partition the reals into positive and negative, each with their own "rule for roots". This is not nice.
So rather have have one rule for the roots of positive numbers and another for those of negative numbers, it would be far better to define the imaginary unit as i<sup>2</sup> = 1.
The impact on calculations is, of course, negligible. But it is more hygienic!
imaginary numbers are fun
(a+bi)(c+di) is the multiplication of 2 complex numbers, just use ordinary math to solve it with the addition of i²=1
Quaternion is even more fun
they arent Commutativity in multiplication and division[/quote]
lets not forget the Octonions, those aren't even associative.
yes there is fun for everyone when it comes to imaginary numbers.
yeah lets party
the real party is in finding a practical use for Octonions. seriously whats the deal with there existance?
and Quaternion . they are fun but for what reason except party makes do they serve?
and where does it end? next thing you know theres sednions and other hypernumbers... seems like they don't want the party to end.
nope, seems like it
where did i put the party hats?
(1+3i)(13i) to your rightOriginally Posted by Zelos
I know abou quaternions and what not but what's the principle of octonians, I've wondered myself will people ever stop making up numbers! We have an infinite number of them anyway!
Well, I don't. Please explain them (in detail, if you don't mind).Originally Posted by Robbie
ok, let me try (im not doing maths in college so maybe someoe else could discuss it in more depth) but it was discovered by irish mathematician Wiliiam hamelton who famously thought of it while walking along the grand canal in Dublin one evening.
i2 =j2 = k2 = 1
so:
ij = ji = k
jk = kj = i
ki = ik = j
Quaternions re non commutative, which is properly expresse in matrix form and there's loads of other interesting stuff about them which was not understood at the time of invention (and I still dont!) but mybe if someone could help out...
Quaternions are important in computer graphics since they can represent 3D rotations in a very nice way (IMHO, much nicer than any other way I've seen). Full details here.
I don't see the "so", bolded in yours. Anyway that much I can read anywhere, but thanks for the attempt  it's just that you came on like an expert.Originally Posted by Robbie
his thing is a bit wrong the correct thing is
i²=j²=k²=ijk=1
well now i'll never look at computer games in the same way ever again.Originally Posted by MagiMaster
thanks for the link.
Originally Posted by wallaby
That's what I was thinking. Nice link btw.
I've looked up quaternions numerous times but never got an example for their use, only equations and identities which isnt my strong suit. I have a better idea now to go with those rules.
Magic Squares.
Almost like sudoko but a THOUSAND times better !!!
Um Zelos, your definition and the one given previously are equivalent  so how is his wrong?Originally Posted by Zelos
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