Imaginary Definition and 362 Threads

The Function To Be Programmed \sigma_m=\frac{4(n_r^2 -1)J_m(n_r k R)}{\pi^2kD_m^+(kR)D_m^-(kR)} where D_m(z)=n_rJ'_m(n_rz)H_m(z)-J_m(n_rz)H'_m(z). The '+'/'-' superscripts indicate the limits as z approaches the branch cut, which lies along the negative imaginary half axis, from the positive...

Hi there, I'm having trouble understanding the Fourier transform of a function where the result in the frequency domain has imaginary components. For example, if you take the Fourier transform of Sin[t] , the result is I Sqrt[\[Pi]/2] DiracDelta[-1 + \[Omega]] - I Sqrt[\[Pi]/2]...

needed help to solve this math home work? Please help.. What is the value of log(i*pi/2) ? I know the answer is "i*pi/2", but don't know the procedure to solve it. Please help me. Thanks a lot in advance.

is there a way to solve this without performing the tedious expansion of $(1+j)^8$? here's the problem $\text{Im}[(1+j)^8(x+jy)]$

While investigating more about complex numbers today I ran across the 2x2 matrix representation of a complex number, and I was really fascinated. You can read what I read here. As I understand it, you write z in its binomial form but instead of "1" you use the identity matrix, I, and for i...

Homework Statement Multiply the matrices to find the resultant transformation. $$x\prime =2x+5y\\ y'=x+3y $$ and $$ x\prime \prime =x\prime -2y\prime \\ y\prime \prime =3x\prime -5y\prime $$ Homework Equations $$Mr=r\prime$$ The Attempt at a Solution I get imaginary eigenvalues of -i and...

Trying the already known equation, sin^2(x) + cos^2(x) = 1 i wondered what would happen if i took that either sin(x) or cos(x) squared equalled a number greater than 1, so when i plugged in sin(x) as 5/3 i got cos(x) 4i/3 , went to euler's equation and added the results, then put the...

Homework Statement Image Attached Homework Equations Impedance/Reactance Mesh Analysis The Attempt at a Solution KVL -V + 2I1 + 4.7(I1 - I2) + j2(I1 - I3) = 0 4.7(I2 - I1) - j0.056(I2) + 2(I2 - I3) = 0 j2(I3 - I1) + 2(I3 - I2) + I3 = 0 (4.7 + j2)I1 - 4.7I2 - j2(I3) = 4V 4.7(I2-I1) -...

I never see the following hypothesis but I believe that they are true... ##\text{Re}(\hat f (\omega)) = a(\omega)## ##\text{Im}(\hat f (\omega)) = b(\omega)## where: ##f(t) = \int_{-\infty}^{+\infty}\hat f(\omega) \exp(i \omega t) d\omega = \int_{0}^{\infty} a(\omega) \cos(\omega...

In euclidean quantum field theory, the imaginary part of the free energy, defined as the logaritm of the partition function, is it connected to the decay rate?

I have a partition function in euclidean quantum field theory. I have a parameter, let's say a charge, that I can change in the action that define the partition function. I found that for small charge the partition function is positive, but there is a critical charge, above the one the...

Homework Statement I have to find the Thevinin Equivalent for the following circuit. I am assuming the current is going out of the node. V= node between inductor and capacitor V0 = V[40/(40-150j)] (V-75)/(600+150j) + (-0.02V0) + V/(40-150j) = 0 The only problem I have is with the last...

Homework Statement f:\ v(x,y)=4xy+2x The task is to calculate the imaginary part. Homework Equations The Attempt at a Solution I have no idea what to do because in my opinion u(x,y) can be anything. For example: f(x,y)=4xy+2x+(3x-4y)\text i. But I must be wrong. I would...

I know what a complex number is. Learned it way back when I took college classes. I know it is a number that has a real and imaginary part of the form a + bi. What I have always failed to understand is what conceptually does it mean. I know what i is , it's the square root of -1. I just could...

Homework Statement How would you define a number that is raised to an imaginary power? Homework Equations λi= ? λ = 6+4i The Attempt at a Solution eln x = x Other than that I have absolutely no idea how to go about solving this.

I am not good at maths but very passionate about physics (I know is sad). I am trying to imagine how strong (or weak) the force of gravity is, so I have this imaginary experiment: [BWe have to stones of, let's say, one kilo each floating in a void, separated by let's say one meter. In absence...

When i is defined by an equation which has 2 solutions, how does it make sense to do algebra with complex numbers?

Homework Statement Find the real and Imaginary parts of sin(3+i) Homework Equations sin(x+y)= sinxcosy+sinycosx The Attempt at a Solution I think I am right in saying that you use the sine addition formula but then i get stuck from there. Is it something to do with exponential form?

I'm trying to decide if the modified Bessel function K_{i \beta}(x) is purely real when \beta and x are purely real. I think that is ought to be. My reasoning is the following: \left (K_{i \beta}(x)\right)^* = K_{-i \beta}(x) = \frac{\pi}{2} \frac{I_{i \beta}(x) - I_{-i \beta}(x)}{\sin(-i...

I'd like to evaluate the integral, \int^{i\infty}_{-i\infty} \frac{e^{iz}}{z^2 + a^2}dz along the imaginary axis. This function has poles at z = \pm ia , with corresponding residues \textrm{res}(\frac{e^{iz}}{z^2 + a^2},\pm ia) = \pm\frac{e^{\mp a}}{2ai} My question is - I'm not sure...

Homework Statement Determine the real part, the imaginary part, and the absolute magnitude of the following expressions: tanh(x-ipi/2) cos(pi/2-iy) Homework Equations cos(x) = e^ix+e^-ix tanh(x) = (1-e^-2x)/(1+e^-2x) The Attempt at a Solution for cos(pi/2-iy)=...

Homework Statement Using the imaginary parts When using complex representation, it is customary to use the real parts. Instead use the imaginary part of e^{j\theta} to calculate an expression for the sum: \sin(\omega t) + \sin((\omega + \Delta \omega)t) Remember, it should come out to...

I have a working DFT and FFT now that I coded in a program .. now from testing I can see that with both the FFT and the DFT if I just graph the Imaginary number I will get the right frequency for example: F[t] = 10 Sin((2 * PI * 2000 *t)/8000) 0 <t <1024 will get me a frequency 2000...

I wanted to do this integral $$\int_a^b \frac{dx}{1-x^2} $$ and I was able to get the right answer with the substitution u=ix, where i is the square root of -1. But is this a valid mathematical procedure? $$\int_a^b \frac{dx}{1-x^2}=i \int_{-ia}^{-ib} \frac{du}{1+u^2}$$ Do those limits...

If f:C-->C is holomorphic and , find the real and imaginary parts ug and vg of g in terms of the real and imaginary parts uf and vf of f.

Hi; How to raising a square matrix to the power of a complex number? for example: [1 2;3 4]^(1+i) or mathematics software such as Scilab how solve such problems? -->[1 2;3 4]^(1+%i) ans = - 0.1482039 - 0.2030943 - 0.3046414 - 0.4528453 Thanks in advance...

Find all possible Values of: 2(-i)

Homework Statement Consider a vector z defined by the equation z=z1z2, where z1=a+ib, z2=c+id. (a) show that the length of z is the product of the lengths of z1 and z2. (b) show that the angle between z and the x-axis is the sum of the angles made by z1 and z2 separately. The Attempt at a...

So I'm reviewing some mathematics for quantum mechanics and this came equation came up \int_{-\infty}^{\infty} a \left( k \right)^{*} i \dfrac{d\,a\left(k\right)}{dk}dk. If a \left( k \right) is constrained to be real then this integral is zero or so the text says. Why is this the case...

Homework Statement I'm in this self-learning course. I came on this problem I thought of. So, i^2=-1. But, isn't i=sqroot of -1? If so, the product of the two minus -1 and the square root of that should give 1. Am I not getting something? I searched the web with the keywords of my...

Homework Statement Determine the general solution of: y(6) + y''' = t The Attempt at a Solution Ok, r = 0, 0, 0, 1/2 +- 3i/√2, -1/2 + 3i/√2 What do I do with that last r value? It turns into ce-t somehow, but I don't see it. edit: typed a number in wrong, fixed now~

What would be the implications of assuming the existence of an imaginary number that can divide a prime number and is related to the number it is dividing? By imaginary I mean a number that is just in our imagination and not the imaginary number "i".

Hey guys. I'm trying to comprehend the TEmn EM fields in wave guides. I've gone through the derivation, using Pozar's microwave textbook, and for the most part it's straight forward. I am having a hard time though determining what the effect of the imaginary factor in the field equations are...

Homework Statement The energy level scheme for the mythical one-electron element crazyidium(the names not really relevant). The potential energy of an electron is taken to be zero at an infinite distance from the nucleus (a) How much energy does it take to ionize an electron from the ground...

Show that, \[\mbox{Im}(f(z))=\frac{1-|z|^2}{|z-i|^2} \mbox{ where }f(z)=\frac{z+i}{iz+1}\] \begin{eqnarray} \mbox{Im}(f(z))&=&\frac{1}{2i}(f(z)-\overline{f(z)})\\ &=&\frac{1}{2i}\left(\frac{z+i}{iz+1}-\frac{\overline{z}-i}{-i\overline{z}+1}\right)\\...

At about 7:00 he talked about imaginary time. Does that account for parallel universe? Also is there an imaginary mass as well?

Let me start by writing about the natural or counting numbers. The story of how, where and when we invented them is lost in the misty dawn of history. But perhaps our African ancestors, like our living simian cousins (and some other animals) evolved the ability to distinguish between few and...

Everybody says that it is used in engineering or somewhere but how can you use it. in real world it is impossible to take square of any number and get negative answer. how can it have any use when it does not even exist. and people talk about imaginary plane, what is it? Thanks for helping...

There is a type of exchange of particles which is generalised by a type of potential: \frac{e^{-\alpha\r}}{R} This potential is used to explain the exchange of bounded particles (e.g a poin between neutron and proton) between two possible configurations. The potential comes from the fact that...

The solutions, in the position basis, of the Schrodinger Equation for the Quantum Harmonic Oscillator are a family of functions based on the Hermite Polynomials. The Wikipedia link for this subject is http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator . But this Wikipedia article and...

z = h(x) + ig(x) True or False: By the definition of the complex plane, h(x) and ig(x) will always be orthogonal. If this was true, wouldn't that mean that we can find a 'very general' Fourier series representation of any function f(x) as an infinite series of An*h(x) + infinite series of...

Homework Statement Find the polar form for zw by first putting z and w into polar form. z=2√3-2i, w= -1+i Homework Equations Tan-1(-√3/3)= 5∏/6 The Attempt at a Solution r= √[(2√3)2+(-2)2]=4 tanθ= -2/(2√3)=-1/√3=-√3/3=> acording to above... tan-1(-√3/3)= 5∏/6 so, in polar form z should be...

Homework Statement Show that \int_{\gamma}\ f^*(z)\ f'(z)\ dz is a pure imaginary for any piecewise smooth closed curve \gamma and any C^1 function f whose domain contains an open set containing the image of \gamma 2. The attempt at a solution I have tried to approach it from some...

Homework Statement Derive the following relation, where z1 and z2 are arbitrary complex numbers |z1z2*+z1*z2| ≤ 2|z1z2| The Attempt at a Solution I found the expression |z1z2*+z1*z2| = |2(a1a2+b1b2)| = √(4[a12a22 + 2a1a2b1b2 +b12b22]) But that is where I get stuck. How does the...

Why does the incomplete gamma function have an imaginary component, when the exponential integral does not? \Gamma(0,z,\infty)\equiv\int^\infty_z \frac{e^{-t}}t dt Ei(z)\equiv-\int^\infty_{-z} \frac{e^{-t}}t dt Looking at how these integrals are usually defined I would have expected them to...

1. -xn2+2(k+2)x-9k=0 Has two imaginary roots, what are the values of k? Attempted to break it down and use the quadratic formula but wasn't able to do it. Would like a pointer in the right direction of where to begin to solve it. Thanks

Hi, What should be the influence of the imaginary part on a complex number? I am asking because I am running a simulation model where the input is a complex number; say z=a+ib Now the problem is that I get the same result when I put a=0 and give some high value to b, as when I do the...

How do I find the imaginary part of $\displaystyle \frac{1}{i}xe^{-ix}+e^{ix}$?

Hi, my question is, if there is an interpretation for electromagnetic gauge fields, whose components are imaginary. This would lead to an imaginary magnetic field... Does anything like this exist? Or is it forbidden ny some first principal arguments? Thank you in advance for every input! Melvin

Homework Statement when I am solving quantum problem, i see an equation like e^(-kx) e^(icx) i is imaginary. how can i take the integral and derivative of this function Homework Equations e^ix ) cosx + isinx The Attempt at a Solution actually i tried e^x(-k+ic) and i said the...