Conjugate Definition and 247 Threads

Hi, an exercise asks to show that $ \int_{0,0}^{1,1} {z}^{*}\,dz $ depends on the path, using the 2 obvious rectangular paths. So I did: $ \int_{c} {z}^{*}\,dz = \int_{c}(x-iy) \,(dx+idy) = \int_{c}(xdx + ydy) + i\int_{c}(xdy - ydx) = \frac{1}{2}({x}^{2} + {y}^{2}) |_{c} + i(xy - yx)|_{c}...

Hi, I am not sure what $ {f}^{*}({z}^{*}) $ means? I think the '*'s cancel, ie $ {f}(z) = u(x,y) + iv(x,y), \: \therefore f({z}^{*}) = u(x,y) - iv(x,y), , \: \therefore {f}^{*}({z}^{*}) = u(x,y) + iv(x,y) $ ? Thanks

Homework Statement You need to produce a buffer solution that has a pH of 5.70. You already have a solution that contains 0.0200 moles of acetic acid. Using the Henderson-Hasselbalch equation calculate the moles of sodium acetate needed to create a buffer with the desired pH? The Ka of acetic...

Question Find the posterior probability that the next two observations y4 and y5 will both be zero? Where the prior distribution is a gamma with parameters (a,b) and the sample is of size of 3 taking from a poisson disribution with parameter V. So far I have shown that the posterior...

I have answered all parts of the following question except for the very last sentence: 'Conclude that the number of elements in X_K is a divisor of |K|.' MY THOUGHTS Presumably I must argue that ord(K*) divides ord(K). Clearly Ord(K*) =< ord (K). Also I can show that for any element Na in...

Hello everyone. At first, I appreciate your click this page. I have a book named 'A first Course in Abstract Algebra 7th' by Fraleigh. I have a question about 'relation algebraic property with conjugate' in automorhisms of fields. in page415, this book explains "Let E is algebraic extension...

Hi there! As you might have already guessed, I'm referring primarily to the 'geometrical' difference (is there such geometry in Hilbert space?) between ##n##-dimensional state vectors | \psi \rangle = \left( \begin{matrix} \psi_1 \\ \psi_2 \\ \vdots \\ \psi_n \end{matrix} \right) and their...

Looking for the general equation for repeated complex conjugate roots in a 4th order Cauchy Euler equation. This is incorrect, but I think it is close: X^alpha [C1 cos(beta lnx) + C2 sin(beta lnx)^2] I think that last term is a little off. Maybe C2 sin [beta (lnx)] lnx ?

Q. Prove there is a one-to-one correspondence between the set of conjugates of H and the set of cosets of N. I have a solution to this below but am not sure if it is correct. In particular I am not sure if my definition 'f' is satisfactory. This is self study and not any kind of homework. I...

I know that (A\mp )\mp =A . Where A is an Hermitian operator How does one go about proving this through the standard integral to find Hermitian adjoint operators? I should mention, I don't want anyone to just flat out show me step by step how to do it. I'd just like a solid starting place...

I'm just starting this, but what would the complex conjugate of Ψ(x,t) in the equation : |Ψ(x,t)|^2= Ψ(x,t)* Ψ(x,t) be.. Let's just say, for example, that x is 4 and t is 9... Please help if you can.. Could you please help me out with the steps to completing this, because I really want to...

Prove: Let \alpha = (a_1,...,a_s) be a cycle and let \pi be a permutation in Sn. Then \pi \alpha \pi ^{-1} is the cycle (\pi(a_1), ... \pi(a_s)) My attempt. (\pi \alpha \pi ^{-1})^s = (\pi \alpha^s \pi ^{-1})=e so if this thing is a cycle and its length divides s. Assume \pi (a_1) is a...

Given an element a in a group G, class(a) = {all x in G such that there exists a g in G such that gxg^(-1) = a} class(b) = {all x in G such that there exists a g in G such that gxg^(-1) = b} so let's say y is a conjugate of both a and b, so it is in both class(a) and class(b), does that mean...

Homework Statement prove that sqrt2|z| greater than or equal to |Rez| + |Imz| Homework Equations |z|^2 = x^2 + y^2 Rez=x, Imz=yThe Attempt at a Solution so far I've worked it down to this. 2(x^2 + y^2) greater than or equal to x^2 + 2xy + y^2 I've used a few different values for x and y and...

Homework Statement In Sakurai's Modern Physics, the author says, "... consider an outer product acting on a ket: (1.2.32). Because of the associative axiom, we can regard this equally well as as (1.2.33), where \left<\alpha|\gamma\right> is just a number. Thus the outer product acting on a ket...

If you have the product of two Grassman numbers C=AB, and take the conjugate, should it be C*=A*B*, or C*=B*A*? The general rule for operators, whether they are Grassman operators (like the Fermion field operator) or the Bose field operator, I think is (AB)^dagger=B^dagger A^dagger. This...

Hi, so I'm a first year neuroscience student at Carelton University in Canada. I had a little bit of a "revelation" with this topic recently after I understood it a bit better and I think this is really interesting. (If I understand it correctly!) We're learning about Kekule structures...

\(u = 2x(1 - y)\) I want to find v such that \(f = u +iv\) is analytic. The hint is find the conjugate function of u. I am not sure if what I did was finding the conjugate function of u thoug. \[ u_x = 2(1 - y) = v_y \] so \[ v = 2y - y^2 + g(x) \Rightarrow v_x = g'(x) \] and \[ u_y = -2x =...

Homework Statement Find U(x,y) and V(x,y) for f(z) = -(1-z)/(1+z) Find Ux, Vy, Vx, Uy (partial derivatives) Homework Equations z = (x+iy) The Attempt at a Solution I found U(x,y) and V(x,y), and I used the quotient rule to find the partial derivatives Ux, Vy. They should be...

I'm confused about some of the notation in Hoffman & Kunze Linear Algebra. Let V be the set of all complex valued functions f on the real line such that (for all t in R) f(-t) = \overline{f(t)} where the bar denotes complex conjugation. Show that V with the operations (f+g)(t) = f(t) +...

Homework Statement Are f(x)=2x, x\in R and g(x)=x^2, x>0 topologically conjugate? i.e. does there exist an h(x) such that h(g(x))=f(h(x))The Attempt at a Solution My professor gave one example in class about finding such a function h which was by guessing it to be equal to xn and...

Dear all, I was reading "Nature of space and time" By Penrose and Hawking pg.13, > If $$\rho=\rho_0$$ at $$\nu=\nu_0$$, then the RNP equation > > $$\frac{d\rho}{d\nu} = \rho^2 + \sigma^{ij}\sigma_{ij} + \frac{1}{n} R_{\mu\nu} l^\mu l^\nu$$ implies that the convergence $$\rho$$ will become...

Homework Statement Two subgroups of G, H and K are conjugate if an element a in G exists such that aHa^-1= {aha^-1|elements h in H}= K Prove that if G is finite, then the number of subgroups conjugate to H equals |G|/|A|. Homework Equations A={elements a in G|aHa^-1=H} The Attempt...

Hi I have been looking at the solutions to a past exam question. The question gives the annihilation operator for the harmonic oscillator as a= x + ip ( I have left out the constants ). The question then asks to calculate the Hermitian conjugate a(dagger). I thought to find the Hermitian...

Let ψ be a wavefunction describes the quantum state of a particle at any (x,t), What does ψ* i.e, the complex conjugate of a wavefunction means? I only know probability of finding a particle is given by ∫|ψ|^2 dx= ∫ ψ*ψ dx But what does ψ*ψ really means? I started learning QM with Griffiths...

What is the result of the charge conjugation acting on the state of vacuum? C|0>=... I have two intuitive problems... If I see the vacuum as something which has no particles, then the charge conjugate would have to lead in the vacuum itself... C|0>=|0> However, if I think of the vacuum as the...

In the standard QFT textbook, the Hermitian conjugate of a Dirac field bilinear \bar\psi_1\gamma^\mu \psi_2 is \bar\psi_2\gamma^\mu \psi_1. Here is the question, why there is not an extra minus sign coming from the anti-symmetry of fermion fields?

There is an argument that accurate sequential measurement of conjugate observables A and B on the same state is possible if the state is an eigenstate of one of the observables. When the state is an eigenstate of A, an accurate measurement of A will not disturb the state, so B can then be...

Hi, I know if we have a complex number z written as z = x +iy , with a and real, the complex conjugate is z* = x - iy. Also if we write a complex function f(z) = u(x,y) + iv(x,y), with u and v real valued, then similarly the complex conjugate of this function is f(z)* = u(x,y) - iv(x,y)...

I seem to have a problem understanding this: If 1% of a weak acid dissociates in pure water. I would assume that 99% of it’s conjugate base would dissociate to form HA in pure water, but this is not the case: I tried to set up a situation below: Please help me understand what I’m...

Hi all! From Wirtinger derivatives, given z=x+iy and indicating as \overline{z} the complex conjugate, I get: \frac{\partial\overline{z}}{\partial z}=\frac{1}{2}\left(\frac{\partial (x-iy)}{\partial x}-i\frac{\partial (x-iy)}{\partial y}\right)=0 This puzzles me, because I cannot see why a...

I have seen it thrown around a lot that the pH at which concentration of a conjugate base is at a maximum can be found by adding up the 2 pKa's whose reactions that base is involved in and dividing by 2. But I tried differentiating and this only appears to be the case for HA- maximum...

Homework Statement This is not exactly a HW problem but related to my thesis work where I am deriving an expression for the intensity of light after a particular spatial filtering. I have: I(x) = \left[ comb(2x) \ast e^{i\Phi(x)} \right] \left[ comb^*(2x) \ast e^{-i\Phi(x)} \right] Where...

Hi, I know this question may seem a little trivial, but is there any real difference between \left (\partial_{\mu} \phi \right)^{\dagger} and \partial_{\mu} \phi^{\dagger} and if so, could someone provide an explanation? Many thanks. (Sorry if this isn't quite in the right...

what is the dot product of two complex conjugate vectors?

Digital signal processing -- conjugate reciprocal of a complex number what is the difference between conjugate of a complex number and conjugate reciprocal of a complex number i am asking with reference to z transform...Thanyou

Hi guys, getting a little confused whilst looking through a paper. I was hoping someone could clear this up for me quickly; If we have a matrix denoted by the following, which is both real and unitary; Amn then is the following true (due to it being real, the conjugate just produces the...

Good Day, I would like to know how to find the complex conjugate of the complex number 1/(1+e^(ix)). I got (1+e^(-(ix)))/(2+2 cos x) but the solution is 0.5 sec (x/2) e^(i(x/2)). Any help will be greatly appreciated. Thanks & Regards P.S. Apologies for not using LATEX as it was formatting...

Consider the following commutator for the product of the creation/annihilation operators; [A*,A] = (2m(h/2∏)ω)^1 [mωx - ip, mωx + ip] = (2m(h/2∏)ω)^1 {m^2ω^2 [x,x] + imω ([x,p] - [p,x]) + [p,p]} Since we have the identity; [x,p] = -[p,x] can one assume that.. [x,p] - [p,x] =...

Im doing some complex variable "counter integration" problems and this one came up. I = \oint e ^{\frac{z}{\overline{z}}}dz the integral must be done over a circle with radio r My first attempt was to do it in the exponetial form, so we have this: \frac{z}{\overline{z}} =...

Can someone conceptually explain to me how Temperature and Entropy are conjugate variables? I would imagine that Temperature and Internal Energy would be more appropriate, as I understand Heat flow causes changes in Internal Energy, some of which is used to change the translational motion of...

Hi, I need to understand the proof about complex conjugate of a function. g(z) = g*(z*) I don't know what it it called in English and can't search for it. If anyone knows where can I get the proof, please let me know. Thanks for help.

Hi Guys, I have two questions which kind of relate. The first relates to the complex conjugate of a function. Specifically, When a function is multiplied by its complex conjugate, what does that mean physically? For instance, I am reading a book on electromagnetic wave scattering, and often...

I'm having trouble figuring out how a field and it's conjugate are independent quantities. How can they be, when they are related by conjugation? Suppose you have real fields x and y, and form fields: L=(x+iy)/sqrt2 R=(x-iy)/sqrt2 In a path integral, you'd have .5(∂x∂x+∂y∂y) in your...

Homework Statement Hi I have a complex function of the form \frac{1}{1-Ae^{i(a+b)}} I want to take the complex conjugate of this: The parameters a and b are complex functions themselves, but A is real. Am I allowed to simply say \frac{1}{1-Ae^{-i(a^*+b^*)}} where * denotes the c.c.? I...

Homework Statement Let G be a group of odd order, and a an element of G (not identity). Show that a and a^-1 are not conugate. Homework Equations The Attempt at a Solution The only hint I have is to consider action of G on itself by conjugation.

Question about matrix groups and conjugate subgroups? This question concerns the group of matrices L = { (a 0) (c d) : a,c,d ∈ R, ad =/ 0} under matrix multiplication, and its subgroups H = { (p 0, (p - q) q) : p,q ∈ R, pq =/ 0} and K = { (1 0, r 1) : r ∈ R}Show that one of H and K is a normal...

Homework Statement -\frac{1}{2}[cos(\frac{\pi+\pi n}{\pi+\pi n}) + cos(\frac{\pi-\pi n}{\pi-\pi n})] Homework Equations cos(u)cos(v) = \frac{1}{2} cos(u+v)+cos(u-v) The Attempt at a Solution I am attempting to use the above trig function to simplify the first function, but I can't seem to...

Hi guys, I am having a very stupid problem. I can't figure out what Mobius transformation represents T(z)=z*, where z* is the complex conjugate of z. In my book we are learning about Mobius transformations and how they represent the group of automorphisms of the extended complex plane (Ʃ). [...

Homework Statement So we are given \alphaexp(i\varpit) +\alpha*exp(-i\varpit) and are asked to prove the resulting equation is real. Homework Equations \alpha + \alpha* = 2Re(\alpha) and Euler's Identity The Attempt at a Solution I tried expanding out the exp's to cosines and isines but...