does imaginary exist

[Mohan.C]

Hi Guys!
While doing some simple maths i got a conclusion that the value of
i (imaginary # ie. root of -1)
tends to infinity but why do we consider it if that is so
Can any one help me with this

[Guille]

You have yo be carefull when dealing with math of imaginary numbers. Can you give the works that lead you to a value of infinity?

[Mohan.C]

guille i can tell that in the end it went to 0/0 which i think is infinity. But i asked my teacher in our school and he said (i) was a constant cant have such values however I have always been poor in maths

[Guille]

0/0 is considered in undefined in mathematics, just as many operatiosn including 0 or infinity. i is not a number, it is a new dimension of numbers. Imagine all the eal numbers are in the x (horizontal) line of the graph, and all the imaginary numbers are in the y (vertical) line of the graph. 0 is in the middle. 4 is on the right side of x, -4 is in the left side of x. 4i is on the top part of y, -4i is on the botom side of y. Any number which is not on a any of the two lines, but a mixture of imaginary and real numbers, like say the number 4x(3i) is in the graph points, and is called complex number. How old are you? (if I can ask)

[Mohan.C]

0/0 is considered in undefined in mathematics, just as many operatiosn including 0 or infinity. i is not a number, it is a new dimension of numbers. Imagine all the eal numbers are in the x (horizontal) line of the graph, and all the imaginary numbers are in the y (vertical) line of the graph. 0 is in the middle. 4 is on the right side of x, -4 is in the left side of x. 4i is on the top part of y, -4i is on the botom side of y. Any number which is not on a any of the two lines, but a mixture of imaginary and real numbers, like say the number 4x(3i) is in the graph points, and is called complex number. How old are you? (if I can ask)

Whatever u may say Guille but it is hard do believe that symbols have meanings. If we can plot doesn't it mean those are constant. If u must know how i did that just express any no. in the polar form or as (x+iy). multiply them but instead of multiplying with 0. u cross multiply it to the LHS. u will get either i=1/0 or i=0/0.

By the way u can ask my age i am i suppose 14 months elder to you. I know i am poor in maths. Though i like to learn somehow it doesn't get into my head.

[Guille]

Whatever u may say Guille but it is hard do believe that symbols have meanings. If we can plot doesn't it mean those are constant. If u must know how i did that just express any no. in the polar form or as (x+iy). multiply them but instead of multiplying with 0. u cross multiply it to the LHS. u will get either i=1/0 or i=0/0.

By the way u can ask my age i am i suppose 14 months elder to you. I know i am poor in maths. Though i like to learn somehow it doesn't get into my head.

No, I didn't ask your age because I thought your math was ridiculous. I agree it is hard to believe symbols have meaning, but letters are symbols, numbers are symbols... Not only i. Yes, I have used several times and got to i=1/0 and sometimes i=0/0. Probably there is an operation we are doing which is false... Or maybe there is a complex solution that mathematicians have developed?

[baudrunner]

I will briefly try to explain imaginary and complex numbers.

In certain scientific applications, in my example I will use electronics since it encompasses all sciences, it is found useful to use imaginary numbers, particularly with respect to solving electronic circuits. I will begin by discussing the j operator (it is the same as i in non-electronic applications). The j operator is used to denote rotation of 90° in the counterclockwise direction. For example, on the X-Y graph a line a units long can be operated on by the operator j to become ja, a line of the same length as before but rotated 90° in the counter clockwise direction to lie on the Y axis. Any quantity operated on by -j will rotate through 90° in the clockwise direction. The quantity j(ja) is written j²a, and j(j(ja)) is written as j³a. So j²a becomes -a. Things become interesting when we analyse the situation where j-ing a twice in succession brings it to the same point as a single operation with a minus sign therefore j²=-1 and we can therefore conclude that j=sqr.rt -1. j³ must equal j(-1) or -j, and j^4 must equal j²•j² = (-1)(-1) = +1.

In mathematics, the square root of a negative number is known as an imaginary number. Its terminology is misleading because in dealing with some scientific applications imaginary numbers become real. In order to avoid difficulty in dealing with square roots of negative numbers we consider that every imaginary number can be expressed as the product of a positive number and the sqr.rt of -1, for example the sqr.rt of -25 is sqr.rt -1•sqr.rt 25 = sqr.rt -1•5. We can then write this expression as j5.

The term complex number refers to an expression wherein an imaginary number is united to a real number by a plus or minus sign. 3-j4 is a complex number.

All operations can be performed on complex numbers. It is not within the scope of this discussion to give examples of their actual application in electronic circuit problem solving as that would be going too far, but trust me, these imaginary numbers are quite real when used practically.

[Mohan.C]

Well i don't get the point still. If u are saying that imaginary could be used can also infinity be used practically. I doubt it

[baudrunner]

It's just more math, Mohan. Insomuch as -. +, x, / etc are operators, j or i are also operators, as described above, and they have a practical use in problem solving in the real world. It is not hard to "get" at all, since the explanation is quite clear as far as it goes and it is not necessary to show how it is used in the practical sense if you can't get past that.

Infinity is a concept, and can only be used in establishing a range in limit calculations, something you won't cover in your academic courses for some time. My suggestion is to stay with the current course curriculum and don't jump ahead of yourself. The explanations will come in time if you have good instructors.

[hanzoganz]

The beauty of complex numbers is, in the first place, that they use the imaginary numbers, i.e., numbers that somebody, somehow, had to invent when he ran out of resources to try to explain certain solutions. The complex analysis we learn in high school, as much of the math, doesn´t have anything to do with the real use of these little invented fellows. Complex analysis can be used to solve equations that wouldn´t have an answer in the real plane and, for our special interest in TOE, it is significantly usefull that the complex sphere with the union of the infinite forms a space where solutions can be solved algebraically easier. Then we can use projections to return to the original space. This allow us to work with several dimensions and, even though we can not visualize them, they make sense mathematically.

So, let´s think that math uses a lot of imagination. In the other hand, if the results of an operation yield to different results, we are facing a fallacy. I would like to take a look to that fake operation you guys are trying to solve.

In the meantime, let´s enjoy the power of imagination.

regards,

or