Imaginary numbers Definition and 78 Threads

How does one go about solving the first and second problems of this quiz? http://www.wiziq.com/online-tests/3503-algebra-iit-jee

For example, is 5i "divisible" by 5? Or does divisibility only apply to integers? On that note, is 5pi divisible by 5? Is 5/6 not divisible by 5? Thanks in advance! =)

Im doing A-level maths at the moment an its nowhere in the sylabus I am just generally interested :D can anyone giv me like a really simplish explanation :D cheers

Homework Statement Solve for all values of x both real and imaginary 1) x^3=-8 2)(3/x+1)+(x/x-1)=(x-5/(x+1)(x-1)) 3)2x^3-8x^2+5x=0 4)x^4-7x^2+12=0 5)x - sqroot ( 6 - 5x ) = 0 6)(absvalue(3x)) + 6 = 10 The Attempt at a Solution I tried all of them but came out with wonky answers or I...

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...

Rafael Bombelli first used them and at the time they were thought to be useless. with other discplines (notably physics) finding a use for 'imaginary' numbers, why wasn't it's use curtailed? afterall if I was paid to fill a room with a 1000 people and could only manage 500. would i be within my...

Hi, Just reading through a good physics book about games and came across some stuff on complex numbers. The book states that the following statements are true. i*j*k=-1 I have a problem with this one. Surely doesn't this mean the same as: -1*sqrt(-1)=-1 or -k=-1 How is minus...

Something has been puzzling me...what is an imaginary number in real life? I know that engineers sometimes use it but how do they apply it to real world situations? How is it anything but a mathematical constant?

In Algebra we are learning and using imaginary numbers. Someone asked if imaginary numbers are ever used outside of math, and our teacher said he talked to an electrical engineer who used imaginary numbers all the time. Our teacher didn't know how or why they were used in electrical...

Maybe this should be in the philosophy of science/math forum, but i thought it fitted here. Why is it that variables taking imaginary values are inherently unobservable, whereas real numbered variables correspond to observables like position/momentum? As far as I can see there is no a priori...

w=8i I need to put this in polar form but how can i do this since this would be w=8(cos(theta)+isin(theta)) I can't find the angles because tan(theta)=8/0 which of course is undefined. Is there something that I am doing wrong?

Homework Statement Consider the simplified wave function: \psi (x,t) = Ae^{i(\omega t - kx)} Assume that \omega and \nu are complex quantities and that k is real: \omega = \alpha + i\beta \nu = u + i\omega Use the fact that k^2 = \frac{\omega^2}{\nu^2} to obtain expressions for \alpha and...

what is the absolute value of imaginary numbers, why not "queer" numbers? the square root of -1 is "i". the absolute value of an interger is itself, and of a negative number, it is a positive interger. |-5| = 5 |5| = 5 what is |5i| = ? |-5i| = ? why not invent a queer number...

This is a physics problem but I am having trouble factoring this matrix. Basically, there shouldn't be anything left inside the matrix except 0's, 1's, or i's (any of which can be negative). This seems like such an easy problem but I cannot find something that works. Any ideas? \frac {1}...

Hi, I'm not sure if this is calculas based or algebra based so here's the question. ( (A) 2i, -2i For this question i don't know what is being asked so i guess the pairs could be x... I know this: ax^2+bx+c, a(x-h)^2+k and a(x-s)(x-t) So the problem is how can i use the things that i...

I have 2 equations, imaginary ones, and 2 unknowns...trying to solve for them..but the answer i got, works with one, but not the other: i*Z1 - i*Z2 = -2 - i Z1 + 3i*Z2 = 4 + 7i where i is the imaginary number, and Z1 and Z2 are the 2 unknowns the answer i got: Z1 : 1.33333 +...

My teacher in the charter school I go to wanted to be a mathematition. He said calculus was no problem for him and he got past vector calculus, although he can't remember because it was so long ago. He said he got stuck on imaginary numbers past the caluclus level and this made him quit is...

Dear All, Why do we introduce complex numbers when talking about the voltage behaviour through capacitors and inductors. Any help would be appreciated, Thanks

I have a very simple question. What are Imaginary Numbers (i.e. \sqrt[4]{-16}=2\mbox{i}) used for in mathematics besides negetive roots with an even index? Thank you in advance... ---- Life is a Problem... SOLVE IT!

Why was i invented?

It is known that it was Descartes the one that gave the symbol i the connotation of imaginary; in electrical engineering there is the concept of apparent power(MVA) S = P + i Q where P(MW)=generation or consumed power and Q(MVAR) = reactive power and they both can be measured, so they...

So I understand what a hermitian operator is and how if A and B are hermitian operators, then the product of AB is not necessarily Hermitian since *Note here + is dagger (AB)+=B+A+=BA I also recognize that (AB-BA) is not Hermitian since (AB-BA)+=B+A+-A+B+ In addition, I know that...

Sorry if this isn't the right forum, I didn't know so I just went to general. Could someone explain how this i (imaginary numbers) thing works? I know i is supposed to be a number which is the sqrt of a negative number, which isn't supposed to exist, but what's its use? And yeah...really any...

I've been doing a lot of thinking about imaginary numbers lately. My first question was "What is sqr(i)?". I thought it was unsolvable until I punched it into my trusty (and often right) caclulator and found out it was (sqr(.5)i + sqr(.5))^2 So obvious now. Of course. Anyways, a...

Question: Use the formula cos(x + iy) = cos(x)cos(iy) - sin(x)sin(iy) to find two imaginary numbers whose cosine is 3 My workings so far: cos(x)cos(iy) - sin(x)sin(iy) = 3 Therefore: cos(x)cosh(y) - i(sin(x)sinh(y)) = 3 cos(x)cosh(y) = 3 sin(x)sinh(y) = 0 sin(x) = 0 x = 0...

Could someone PULEEZ explain how to work the following equation: 3-7i/2+3i For the life of me I cannot sqeeze this into my brain! Thank you in advance.

I have an Algebra problem giving me trouble. I am supposed to determine without graphing, if the following equation is symetrical to the x or y-axis or to the origin. The equation is y^2 = -5/x^2. The problem is, I think that this is an imaginary number. Am I right about that?

What are imaginary numbers and how and why are they used in physics? Please could you try and make your answers as simple as possible and bear in mind that I have not even finished my GCSE course in maths yet.