Imaginary Numbers in Math

[ThePatriot]

Would someone please tell my lost friend Jonno here that imaginary numbers can appear in problems. He refuses to believe i is an actual mathematical thing. He says it is a variable...someoen tell him it has a meaning and can be used in a problem.

[synreal]

yup, they exist

http://www.math.toronto.edu/mathnet/answers/imaginary.html

[J]

If I remember correctly, i, the imaginary number is the square root of negative one. Like many things in algebra it is used for something very complicated and useless.

[Jonno06]

i=squareroot of -1.....so therfor its not imaginary in the first place....!

[Jonno06]

This isn't the case. Imaginary numbers do exist. Despite their name, they are not really imaginary at all. (The name dates back to when they were first introduced, before their existence was really understood. At that point in time, people were imagining what it would be like to have a number system that contained square roots of negative numbers, hence the name "imaginary". Eventually it was realized that such a number system does in fact exist, but by then the name had stuck.)

[ThePatriot]

Someone please tell Jonno he is quite mistaken, he is saying its not imaginary, he doesnt seem to understand the dif between a variable and a constant....he thinks i is a constant that is not imaginary. It is imaginary becuase there is no answer for the square root of negative 1, so he says, if it was imaginary it cannot be used in problems. This is coming from someone who is in regular geometry speaking to someone going into Calculus AB...ignorant people...

He was taking it literally...he says that imaginary numbers dont exist, now he says the entire mathematical community as a whole has been mis naming it for as long as its been around. Mid 1700's i believe, could be wrong. Would someone just tell him, please, he refuses to believe me.

[Jonno06]

However, there is a different number system in which such a thing does exist: the Complex Number System. The "numbers" in this different number system will be totally different objects from the familiar real numbers (they will in fact be pairs of real numbers), but that doesn't make them any less real
(0,1)=i
(0,1)(0,1) = ( (0)(0) - (1)(1), (0)(1)+(1)(0) ) = (-1,0)

[synreal]

i is a constant, i is always equal to the square root of -1

it is not imaginary in the sense of not existing, it is "complex", simply meaning we have no easy way of phsyically showing its value

[Jonno06]

i am actually terribly bad at math(failed freshman year)......

i am more of a science type of person actually....

but it sure is fun to debate such a confusing mathematical debate

[ThePatriot]

Yea, in the literal sense it exists, but if you try and determine a value for the square root of negative 1....good luck. Jonno, why dont you tell your math teacher you dont believe that i is imaginary...

[Shaft]

BWA HA HA HA HA HA HA HA
HAHA HA HA HA HAHA HA
AAAAHHHH HAH HAH HAH

Imaginary numbers is my CAREER!!!! As an electrical engineer, currently doing RF (radio) stuff those i's are all I think about. Actually I use j but it's the same thing.

THEY EXIST!!! THEY ARE IMPORTANT!!! THEY ARE GOOD!!!!

Yup yup yup... square root of negative one is what makes it so.

Now you all work with them graphs in algebra right with x and y? I chart stuff in x and i. But I use funky Smith charts of insanity. WA HA HA HA HAHA Wheeeeeeeew

Have a nice day.
Ar

[Jonno06]

how can J be the same thing as I if I is a constant????

[synreal]

the exact same way that i can be james and synreal, call it whatever you want, it has a defined value

[J]

Why the hell do we need imaginary numbers!?!

[Jonno06]

we dont......

can someone give me a problem with i in it please....

[synreal]

Dr. Math -

In our Accelerated Algebra II class, we have been discussing when we
would use the imaginary number "i" in real life. My teacher
recommended you for the answer. I hope you can help us. Thank you!

Sincerely,
Chris Valentine


--------------------------------------------------------------------------------


Date: 11/21/2001 at 08:01:48
From: Doctor Jerry
Subject: Re: When in real life would you use and an imaginary number
(i)?

Hi Chris,

It would be easier to say who doesn't use complex numbers.

Since complex numbers are often called "imaginary numbers," they often
become suspect, seen as mathematicians' playthings. This is far from
the truth, although not easy to prove. If you were to spend some time
in a university library looking through physics, engineering, and
chemistry journals or through books in these disciplies, you would
find many applications of complex numbers. But this is difficult,
since the uses are often buried under a lot of terminology.

Complex numbers enter into studies of physical phenonomena in
unexpected ways. There is, for example, a differential equation with
coefficients like a, b, and c in the quadratic formula, which models
how electrical circuits or forced spring/damper systems behave. A car
equipped with shock absorbers and going over a bump is an example of
the latter. The behavior of the differential equations depends upon
whether the roots of a certain quadratic are complex or real. If they
are complex, then certain behaviors can be expected. These are often
just the solutions that one wants.

In modeling the flow of a fluid around various obstacles, like around
a pipe, complex analysis is very valuable to transforming the problem
to a much simpler problem.

When economic systems or large structures of beams put together with
rivets are analyzed for strength, some very large matrices are used in
the modeling. The eigenvalues and eigenvectors of these matrices are
important in the analysis of such systems. The character of the
eigenvalues, whether real or complex, determines the behavior of the
system. For example, will the structure resonate under certain loads.
In everyday use, industrial and university computers spend a
significant portion of their time solving polynomial equations. The
roots of such equations are of interest, whether they are real or
complex.

[Jonno06]

ok,so the next time i am a University computer firguring out polynomial equations,ill remember to use "i"

[synreal]

whether or not YOU personally use it is irrelevant, it is a real number and it is applied in the real world

for example, that breath you just took, the rate of reduction of air speed moving into your lungs can be plotted as a function of i

[AllAmericanMag]

Brain Fart! AAAHH!!
http://www.geocities.com/johnniemccoy/funnyface2.jpg

[gimp]

jonno06 - Your going to find that there is a lot of stuff in math that you don't think you'll need to use. You'll need a lot of it than you think. Just keep that in mind while your learning the basics here.

[XspyX]

i = squared root of -1
i^2 = -1
i^3 = -i
i^4 = 1

Just did a section on "i" in AlgII. Only use "i" has to me is to simplify equations down another level...dunno bout you guys

[irbodden]

The squareroot of ANY negative number is imaginary as it the Log of ANY negative number.

So far everyone else has been correct as well.

[Jonno06]

if i^4=1,would i be .25??

i would much rather use common sense to find my answers......

i had a question on my home work yesterday....about bags of fertalizer and the area of my house/yard.First we found total area,then subtracted that of the house(since we wont fertalize our house).....and it came out to each bag covers 3500....i looked at all the numbers...and guessed 3...i was right...but even if i baught too many,i could take it back,if i had too less,i could buy more......its just common sence...

[ThePatriot]

Originally posted by Jonno06
if i^4=1,would i be .25??

i would much rather use common sense to find my answers......

i had a question on my home work yesterday....about bags of fertalizer and the area of my house/yard.First we found total area,then subtracted that of the house(since we wont fertalize our house).....and it came out to each bag covers 3500....i looked at all the numbers...and guessed 3...i was right...but even if i baught too many,i could take it back,if i had too less,i could buy more......its just common sence...

He who thinks i^4 = 4 times i isnt very math inclined. I hope you see now, that this conversation is very good, and Jonno isnt the mathematician he proves himself to be.

[Jonno06]

oh,did he mean like "I" to the power of 4???

i thought he meant "i" x 4....

[XspyX]

Means "i" raised to the 4th power.

i^4

[gimp]

Originally posted by Jonno06
if i^4=1,would i be .25??





ah, your logic is a bit flawed there. In that situation, i would be 1 or -1. (1/4)^4 = 1/256.

[SlipknotX556]

I have no idea what you people are talking about. I am failing math right now so dont ask me.

[BTAutoMag]

yes they exist. they are the square root of a negative number.

[ShooterJM]

When I was learning it there were some people that had some issues with i as well.

We were told to think about "i" as direction (form zero) on the number line.

[-Jôker-]

math class in when i eat lunch..... what the heck are you guys talking about!!!! :confused:

[Jonno06]

i am actually smarter than my math teacher in a sense...

i asked her what "i" equaled,and she had no idea what i was talking about...

she can never answer my questions...

[Dubstar112]

In form a+bi, the a is the X value, and the bi is the Y value. I just had a test on these in school. I hate regents math. Only a few states have the Board of Regents. NY, Cali, and i think there is one more.

Now, the regents is being called the Advanced Regents Diploma, and the Local is being called the Regents. Pretty crappy.. Im going for Adavanced regents of course ;)

In a sense, i doesnt equal any thing, it is imaginary. But to relate it to a number, it is the {-sqaure Root} of a number. for example.

{will represent every thing underneat the radical.}

{-32}
{i}{16}{2}
4i{2}

im pretty sure thats how it works, :)

[Miscue]

Complex numbers are VERY important... many many engineering related applications among other things.

Hyperbolic functions (like sinh, cosh... etc.) have 'i' built in, you just don't see it. But you can mathematically convert parabolic functions to hyperbolic with complex numbers.

When you're dealing with electrical circuits and such, you use complex numbers in your formulas to figure out what the circuit is putting out.

Polar coordinate system has a 'real' part and an 'imaginary' part if you ever looked into it.

It is not 'imaginary' in the sense that it is 'fake'. It is not fake, it just is in a category different from 'real' numbers.

[Croix71]

LoL, I haven't touched imaginary numbers since college. :D

[pumpamatic]

It can't exist, my calculator clearly states error when I punch in a negative root. My calculator doesn't lie to me, and it only shows me actual numbers. For those wondering, I'm currently sitting at 97% in Alg 2 as a sophomore.