Imaginary numbers

[Kedas]

Just want to add that in electronics we use the letter 'j' to represent 'i'.

This to avoid confusion with the symbol of current.

 

An ideal capacitor and coil only have an imaginary value because the voltage is exactely 90° out of phase.

Capacitor: Current 90° before voltage or -xj

Coil: current 90° behind voltage or +xj

 

The current of a resistor is in phase and therefore has no imaginary value, you can also say it has one but it is always zero like 0j.

 

Yes, you can multiply/divide imaginary numbers with a calculator.

(you have to convert to an other representation though, real & real -->real & angle, a little calculator programming helps a lot)

[neo_maya]

YT2095 said in post #49 :

neo-mayo, ok so it would fit into the "function" catagory then , yes?

a bit like the reciprocal of 0 = infinity (or at least any number you choose to mention)

 

 

Hey don't attack me - I'm just a crappy head.

 

But here is how I see this -

 

No - it wouldn't fit into a function catagory either. Like the illuminated one said - it's just ........i. And what I understand is - +ve infinity means a number greater than the largest number u can think of and -ve infinity means a number smaller than the smallest number u can think of.

 

Though this brings the question - I heard there were 7 special forms like 0/0, infinity/infinity, 0^0 and several others that can't be defined. And they don't fit even into the catagory of infinity. They are like i, just imaginary.

 

[ Someone please book a sit for me in the mental hospital , I am mad ]

[neo_maya]

neo_maya said in post #50 :

 

 

But if a certain amount of energy is not ordered or useful - then wouldn't that energy transform to some other form of energy? Then why is it irreversible?

 

 

Oooooppsss sorry - got the point of the ever increament of entropy now. So, basically entropy refers to the disorder in the universe - but what is the heat death then?

[JaKiri]

YT2095 said in post #49 :

neo-mayo, ok so it would fit into the "function" catagory then , yes?

a bit like the reciprocal of 0 = infinity (or at least any number you choose to mention)

 

It's not a function.

 

It's a number.

 

You might as well say 'How do you work out 1? Is it the same every time?'

[Kedas]

if everything in the universe would have the same temperature then there wouldn't be any energy transfer anymore.

[YT2095]

and so, if you calculate the sqr rt of -1, what is the answer? in one post you say it`s not a number like "35" and in another you say is IS a number? Kinda WELL LOST here!

[neo_maya]

Ok - I read this in a scinece-fiction book - if u take a right handed golves outside of the universe and then bring it back - it will be left-handed. - Is there any scientific basis of this theory.

[YT2095]

why should the gloves change? definately sounds like sci-fi to me!?

[neo_maya]

YT2095 said in post #58 :

why should the gloves change? definately sounds like sci-fi to me!?

 

 

First, u tell me - what's outside of this universe?

 

[JaKiri]

YT2095 said in post #56 :

and so, if you calculate the sqr rt of -1, what is the answer? in one post you say it`s not a number like "35" and in another you say is IS a number? Kinda WELL LOST here!

 

It's not a real number (ie on the number line from negative infinity to positive infinity).

 

It's just... a number.

[JaKiri]

neo_maya said in post #59 :

 

 

First, u tell me - what's outside of this universe?

 

 

I can categorically say that whatever it is won't be a mirror.

[Kedas]

i^2=-1 not the same as i=sqrt(-1)

 

There is a funny 'prove' about it that says that -1=1

 

i.i=-1

sqrt(-1).sqrt(-1)=-1

sqrt(-1.-1)=-1

sqrt(1)=-1

1=-1

[JaKiri]

No.

 

That's equivilent to saying that -4 = 4, because SQRT(16) = 4

 

SQRT(16) = -4

 

Hence -4 = 4.

[YT2095]

"It's not a real number (ie on the number line from negative infinity to positive infinity).

 

It's just... a number. "

 

HUH? now I`m totaly lost

the only thing I can think of then is that it must be a variable like (n) or X like in a computer program

 

for X = 1 to 10

next x

 

X isn`t a definate number exactly, but at any one time it`ll have a definate value between 0 and 10.

is it that sort of thing?

[JaKiri]

No.

 

It's a number.

 

i is a number.

 

It's not on the number line from - infinity to + infinity, but it's a number just like 1 or 462.

 

i is the symbol that represents it.

[YT2095]

but that sounds SO contradictory, so I`m sure I must be missing something here?

[JaKiri]

i doesn't have a value in the real numbers. Otherwise it would just be that number.

 

As I said, it doesn't feature on a number line; it exists on an Argand plane, which has the usual number line as the x axis and a similar one for the imaginary numbers as the y axis.

[JaKiri]

You may as well say 'Why is 15 not 3?'

[YT2095]

I kinda regret asking now

Thnx for trying anyway Mr-L, appreciated!

[neo_maya]

IMAGINARY NUMBER. There are two modern meanings of the term imaginary number. In Merriam-Webster's Collegiate Dictionary, 10th ed., an imaginary number is a number of the form a + bi where b is not equal to 0. In Calculus and Analytic Geometry (1992) by Stein and Barcellos, "a complex number that lies on the y axis is called imaginary."

 

Chech out these sites. There are a number of them out there. If u want I can search them for u.

 

http://www.friesian.com/imagine.htm

http://www.jimloy.com/algebra/imaginar.htm

 

[These sites have long articles, but by the time u have finished reading them, I think that will do ]

 

_______________________________________________

 

 

An Argand Plane is where u have to axis X and Y both intersecting each other at (0,0) point. X represents all the real numbers from -infinity to +infinity. And Y axis represents the imaginary numbers.

 

ai + b = each and every number that u see. But in the case of real number a = o and in the case of imaginary number a has a value. So, every real number is a kinda imaginary number (sort of , where the imaginary part doesn't exist) only where a = 0.

 

 

Cube roots of unity and their properties :

 

:lcomega: ^3 = 1

1+ :lcomega: + :lcomega: ^2 = 0

 

where, :lcomega: = 1/2 {-1+ sqrt(-3)}

and :lcomega: ^2 = 1/2 {-1- sqrt(-3)}

 

 

There r a whole lot other stuff regarding i, but basically these are the basic ones. An imaginary number has some other properties like - if u multiply two conjugate imaginary numbers - u will get a real number or if u add them u will get a real number. And there is the modulus and argument of imaginary number. You can even work out the sqrt of [ 7-30sqrt(-2) ].

 

 

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The problem with imaginary numbers are that - yet we can't define them. So, no matter how much we can imagine - we will never imagine an imaginary number until someone defines them or describes their characteristics or properties. But it is indeed a number - we just can't understand it - that's why it's imaginary (u have to imagine it).

________________________________________________

 

I don't know if each and every line of what I have written is right. But that's basically what can think of an imaginary number.

 

PS : There r other forms of undefineables (I think) like - 0/0 , infinity/infinity. 0^0, infinty^infinity etc.

[neo_maya]

Hey, I think there should be a sqrt sign in the smilies list - don't you think?

[JaKiri]

x^1/2?

[neo_maya]

MrL_JaKiri said in post #72 :

x^1/2?

 

 

Ooooppppss. Right.

 

 

[neo_maya]

Hey, I was having some problems with differentiation and integration. Can I post them now?

[JaKiri]

Make a new thread