Imaginary Definition and 359 Threads

Homework Statement A one-dimensional system is in a state at time t=0 represented by: Q(x) = C { (1.6^0.5)Q1(x) - (2.4^0.5)Q2(x)} Where Qn(x) are normalised eergy eigenfunctions corresponding to different energy eigenvalues, En(n=1,2) Obtain the normalisation constant C The...

Hi, I am new here and have been lurking awhile. I have been reading Stephen Hawking Theory of Everything and it brought up imaginary time. ( I got this from the library and just saw online he did not endorse this book) It got me thinking. Time is based on Earth's observations to the solar...

Suppose you imagined a vertically aligned surface and with respect to this imagined (massless) surface were two objects shooting towards each other. Suppose these objects both had mass m, and each their kinetic energies (with respect to each other) would be .5mv^2. Suppose they are moving...

Can you use Wick rotation to turn any real variable to an imaginary one, not necessary time, such that your integration converges, and then, return back to the real? I'm not really sure how to use Wick rotation.

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}...

complex plane Hello, I was wondering if there are only specific types of forumlas that you can graph on a complex plane. I mean can you only plot recursive sequences such as the Mandelbrot Set or can you also plot x,y equations while just ignoring the real part of the y output. Thanks, -scott

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...

In my Algebra 2 textbook it says that the imaginary unit finds practical application in electrical engineering. Is that because the imaginary unit is as elusive as electrical charge to rational perception?

Ok, a multiple choice question wants me to: "State the possible number of imaginary zeros of g(x)=x^4+3x^3+7x^2-6x-13." (A) 3 or 1 (B) 2, 4, or 0 (C) Exactly 1 (D) Exactly 3 Using Descartes Rule of Sings I get: Exactly 1 positive zero, 3 or 1 negative zeros, and 0 or 2 Imaginary...

I have to find (a+bi)(c+di) in polar form given that b,c,d>0 and a<0. So I convert each one to polar first. ( (a+b)cis(\arctan(-b/a) + \pi) ) ( (c+d)cis(\arctan(d/c)) ) That's as far as I got. Little help please?

So I'm trying to work-out the real and imaginary parts of a finite product, put P_n = \prod_{k=1}^{n} \left( x_k + iy_k\right) where the x's and y's are real numbers like you would expect.

Does anyone know how to take the derivative of e^((x^2)/i)? Thanks in advance!

I am to find the imaginary part, real part, square, reciprocal, and absolut value of the complex function: y(x,t)=ie^{i(kx-\omega t)} y(x,t)=i\left( cos(kx- \omega t)+ i sin(kx- \omega t) \right) y(x,t)=icos(kx- \omega t)-sin(kx- \omega t) the imaginary part is cos(kx- \omega t) the...

Is "i" Really Imaginary? Complex-number math is very important in quantum physics. Is this because square roots of negative numbers are actual quantities being measured/calculated? Or is it that imaginary numbers aren't occurring for real, but complex math nevertheless represents very...

I am supposed to identify the imaginary part (marked in bold) of each expression, just wanted to see if I got them correct: 1. (1+i)+(1-i) ......0 2. (5+i)+(1+5i) ......6 3. (5+i)-(1-5i) ......6 4. 1+2i+3+4i+5 ......6 5...

I'm having trouble with concept of imaginary mass, i just want to know why do we need the whole concept of tachyons

This is from "Exploring Black Holes" by Taylor and Wheeler. It's a very good book but I struggle not with the math, but the explanations (sometimes) On page B-13 is a frame called "Metric for the Rain Frame", which is a transformation of the Schwarzschild Metric from "bookkeeper coordinates"...

Hi there have i got this right if someone could check please? z=x+\imath{}y Find the real and imaginary parts z+(1/z) sub x+\imath{}y + \frac{1}{x+\imath{}y} if we multiply by x+\imath{}y and i get as the real part as x^2-y^2+1. Have i got this right? Thanks in advance

z=x+\imathy Find the real and imaginary parts z+(1/z)

Hi, When solving the delta potential Schrod. eq in momentum space, one finds that the poles of the wave function correspond to the bound states. This is the same result when solving the hydrogen atom in momentum space. However, the poles are when the momentum is pure imaginary. My...

I've been working with Complex Analysis and have noticed an interesting result. Under what conditions will the following integral be purely imaginary: \int_{a-bi}^{a+bi} f(z)dz It seems to me some type of symmetry is required. Take for example: \int_{1-8i}^{1+8i} f(z)dz where...

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 +...

I saw this thing where someone proved that the imaginary number, i, the sqrt(-1) was equal to 1. here it is: i= sqrt(-1) i^2 = [sqrt(-1)]^2 i^2 = sqrt(-1) * sqrt(-1) i^2 = sqrt(-1*-1) i^2 = sqrt(1) i^2 = 1 so i = 1 I know there's something wrong here but i can't...

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...

Forgive me if I'm being ignorant, but this recently occurred to me. We all know division by zero is undefinfed, but \sqrt {-1} used to be undefined too, until i was created. Has anyone ever proposed an imaginary number to indicate the result after division by zero?

hi here's a questn: "2 vectors acting in same direction have resultant 20 whereas in perpendicular direction resultant is 10. find the vectors." pls. explain the imaginary solution.

A while back, Huckleberry said he liked the show a lot, I watched it. Its great! Mac and Bloo! Yay! I try and catch it every chance I get, I recommend it. :approve: Thanks. :smile:

I was curious about what class would cover those types of Linear DE w Constant Coeff, particularly Hyperbolic Functions and exp z type of things. I remember my lecturer said back in Intro DE that we only covered first 2 types of Auxiliary Equations - real distinct roots and real repeated ones...

Alright.. I admit it. I have an imaginary girlfriend. :bugeye: Since I am obviously completely inept at this sort of stuff, I have resorted to my imagination to solve my emotional woes. Anyone else have imaginary girlfriends, or am I just a freak? :rolleyes:

When I was reading the Landau's The Classical Theory of Fields, I found that when distance of four dimensional space is negative, the time's square should be a negative as well.Then time is an imaginary number. it's SPACELIKE. But what is imaginary time mean on earth? They say that in that...

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

Folks, I was just wondering why I can write: i^{4/3}=-\frac{1}{2}+i\frac{\sqrt{3}}{2} Regards

I need to solve a linear, second order, homogeneous ODE, and I'm using the Frobenius method. This amounts to setting: y = \sum_{n=0}^{\infty} c_n x^{n+k} then getting y' and y'', plugging in, combining like terms, and setting the coefficient of each term to 0 to solve for the cn's. This...

Well I know it can solve for real numbers of X^n+x^(n-1)+ etc etc = 0 But was wondering if it could also solve when there are imaginary numbers involved?... 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?

http://seattlepi.nwsource.com/lifestyle/202632_imaginary07.html :smile: :smile: :smile:

If someone could give me some notes explaining about them that i could follow so i can do my homework and stuff it would be appreciated! I don't understand them at the moment b/c i don't understand the teacher, which is definately my problem. So it would be nice if i could get an explanation...

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...

If you express a wave as a Fourier series like: z(x,t)= \sum _{n=1} ^{ inf.} A_n cos(nk_0 x - \omega (n) t ) Then what is the physical interpretation of a non-zero imaginary part of a component amplitude?

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...

Hey, I was wondering if anyone could explain to me the meaning of "real and imaginary parts of a complex signal"? Thanks Jay

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...

I was outside just now, stargazing with my 10x40 binoculars, as it is an exceptionally clear and beautiful night here today. I was looking east, at Andromeda, when I spotted a moving object. It's apparent size and magnitude was about that of the stars behind. I follow it in my binoculars while...

No one answered my burning questions about imaginary tides...these tides that have me in a bind, so to speak. So, *sniff, sniff* I will just blunder through the essay questions as best I can. Thanking everyone who has helped me all these weeks...I have a test Monday and feel confident...

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...

I was just wondering if anyone knows the rule when taking the derivative of an imaginary number(i). For example: d(ix)/dx=? Thanks:)