Argument Definition and 388 Threads

In my lines i have, ##(4-2i)^2 = (4-2i)(4-2i)## ##r^2 = 4^2 + (-2)^2 = 20## ##r \cos θ = 4## and ##r\sin θ = -2## ##\tan θ =-\dfrac{1}{2}## ##⇒θ = 5.82## radians. Therefore, ##|(4-2i)^2| = \sqrt{20} ×\sqrt{20} = 20## Argument = ##5.82 + 5.82 = 11.64##. also ##|2|## = ##2## and argument =...

Hello, I understand that the sine function take an argument as an input and produced an output which is a real number between 1 and -1. My question is about the argument. I know it can be in either radians or degrees which are different units to measure angle. An angle is the portion of the...

π My take; i multiplied by the conjugate of the denominator... $$\dfrac{z_1}{z_2}=\dfrac{2(\cos\dfrac{π}{3}+i \sin \dfrac{π}{3})}{3(\cos\dfrac{π}{6}+i \sin \dfrac{π}{6})}⋅\dfrac{3(\cos\dfrac{π}{6}-i \sin \dfrac{π}{6})}{3(\cos\dfrac{π}{6}-i \sin \dfrac{π}{6})}=\dfrac{2(\cos\dfrac{π}{3}+i \sin...

Hello all I am trying to solve the following integral with Mathematica and I'm having some issues with it. where Jo is a Bessel Function of first kind and order 0. Notice that k is a complex number given by Where delta is a coefficient. Due to the complex arguments I'm integrating the...

What is the current mainstream interpretation of Newton's bucket argument in regards to "absolute space" or similar concepts? Wikipedia asserts both that Newton's intention may either have been (1) to prove the "metaphysical" existence of something we'd call "absolute space" (i.e. some some...

We have to prove: If ##f: [a,b] \to \mathcal{R}## is continuous, and there is a ##L## such that ##f(a) \lt L \lt f(b)## (or the other way round), then there exists some ##c \in [a,b]## such that ##f(c) = L##. Proof: Let ##S = \{ x: f(x) \lt L\}##. As ##S## is a set of real numbers and...

I am trying to build an argument against a friend (F) who is presently not an anti-vaxxer, but is heading in that direction when he told me that a friend (FF) of his told him (F) that his (FF’s) doctor told him that his Covid mRNA vaccine caused his lymphoma. Of course, FF either misinterpreted...

I have some values and by using them I need to find the RAAN and argument of perigee of a satellite. I have the period, inclination, apogee and perigee (as values not vectors), found semi-major axis and the eccentricity, but facing difficulty on how to proceed on calculating RAAN and the...

Let z = x + iy $$\arg \left(\frac{1+z^2}{1 + \bar z^{2}}\right)=\arg (1+z^2) - \arg (1 + \bar z^{2})$$ $$=\arg (1+x^2+i2xy-y^2)-\arg(1+x^2-i2xy+y^2)$$ Then I stuck. I also tried: $$\frac{1+z^2}{1 + \bar z^{2}}=\frac{1+x^2+i2xy-y^2}{1+x^2-i2xy+y^2}$$ But also stuck How to do this question...

The fallacy in the summary is not covered in the sites discussing eigenvalues, so there must be something blindingly and embarrassingly obvious that is wrong. I would be grateful if someone would point it out. Thanks.

Is it because the current applied to a capacitor will never be time independent? Please help me out🙏

Let: ##z=x+iy## $$z+\frac 1 z =1+2i$$ $$x+iy +\frac{1}{x+iy}=1+2i$$ $$x+iy+\frac{1}{x+iy} . \frac{x-iy}{x-iy}=1+2i$$ $$x+iy+\frac{x-iy}{x^2+y^2}=1+2i$$ $$\frac{x^3+xy^2+x+i(x^2y+y^3-y)}{x^2+y^2}=1+2i$$ So: $$\frac{x^3+xy^2+x}{x^2+y^2}=1$$ $$x^3+xy^2+x=x^2+y^2$$ and...

Hello, I'm reading FLP vol II, and I would appreciate some help to understand the argument supporting Figure 6-6. Basically they claim if a sphere has non-uniform charge distribution whose surface density is proportional to the cosine of polar angle, then this surface charge distribution is...

Hello. I wanted to construct a simple and clear explanation for the relation between the beta function and the critical exponents (divergence of correlation length) close to a critical point. I wanted to check if this reasoning is valid. This is my own rewording of complicated arguments I see...

##\sum\limits_{k=0}^{n-m} \frac{\binom{n-m}{k}}{\binom{n}{k}}\frac{m}{n-k}=1##. Can be derived from question. For ##n\ge m##, pick ##m## marbled out of a set size ##n## labeled from ##1## to ##n##, what is probability distribution of minimum of the number labels on the marbles? The terms is...

A free particle with coordinates as shown has kinetic energy ##T = \frac{1}{2}m\left(\dot r^2 + r^2\dot\theta^2 + r^2\sin^2\theta\dot\phi^2\right)## So we see ##T## depends on ##\theta##. Now suppose we rotate our coordinate system such that only one coordinate ##\theta## changes from...

Either that, or the author is a typical "pop scientist" author that doesn't understand probability too well. https://nautil.us/issue/4/the-unlikely/the-odds-of-innocence

In Feynman lectures vol I, last part of chapter 31, there was this argument about electric field on the other side of the opaque wall with holes. The argument is attached below. I'm having a hard time understanding the claim in the red box. In particular, I failed to see how "fields arrive at...

The energy stored in a current loop equals ##\frac{LI^2}{2}##. From a dimensional argument, it follows that the inductance grows with the size of the loop. This would mean that, if we assume the current stays constant, enlarging the loop would require external positive work, so, the force...

I know that e^-ix = cos(-x)-isin(x), but if we have e^-iwx does that equal cos(-wx) - isin(wx)? Thanks

This is my attempt of the problem Argz = (11π+θ) - 2πn 0 < (11π+θ) - 2πn < π/2 0 < (11π+θ) - 2πn or (11π+θ) - 2πn < π/2 n < (11π+θ)/2π or n > (21π/4 + θ) (21π/4 + θ) < n < (11π+θ)/2π, what i was trying to do was to find the value of n which i thought would help me obtain the value of the...

In Griffith’s section 10.3.1, when proving why there is an extra factor in integrating over the charge density when it depends on the retarded time, he makes the argument that there can only ever be one point along the trajectory of the particle that “communicates” with the field point. Because...

Few days ago, I posted an answer for a mathoverflow question. The question was of elementary nature. The question had a lot of views, and my answer didn't get any upvote. Now since I got a downvote, perhaps there was a (major) mistake somewhere in the argument I posted? Tbh I was reasonably...

I've been thinking about the Michelson–Morley experiment lately and how it would play out with acoustic waves clearly showing the presence of a sonic-ether (well, at least in the case it's not enclosed - the air through which the sound travels has to be exposed to the outside wind ofc). And...

since ##|z|≤3## →##z=0+0i##, therefore we shall have centre##(0,0)## and radius ##3##, find my sketch below,

I think I have something which can make an argument against superdeterministic interpretation of QM. Not that I am keen of disproving it, but I think that arguments even against some fringe ideas may have non-zero value and are anyway entertaining. I'll be glad to see feedbacks/review for...

First, we can think a MZ interferometer as a combination of two beamspliter and a phase shifter(from MIT course "Atomic and Optical Physics II", the paper is "Quantum-mechanical noise in an interferometer"), which evolution matrix is B = {{1,-i},{-i,1}},B dagger and P ={{1,0},{{0,exp{i\phi}}}...

Attempt at solution: Proof of i): Let ##x \in X##. Its clear ##G \supseteq HG_x##. Let ##g \in G##.Then there is ##y \in X## such that ##g \cdot x = y##. Since ##H## acts transitively on ##X##, there is ##h \in H## such that ##h \cdot x = y##. So, ##g \cdot x = h \cdot x##. This gives...

Thinking about Cantor's diagonal argument, I realized that there's another thing that it proves besides the set of all infinite strings being uncountable. Namely: That it's not possible to list all rational numbers in an order such that the diagonal of their decimal representation has an...

Cantor's diagonal argument, essentially, proves (or demonstrates, as I'm not exactly sure if it's considered a mathematically rigorous proof) that the set of all real numbers is uncountable, ie. essentially larger than the set of natural numbers. It does this by, essentially, proof by...

Because this problem is easier to understand with a picture, I'll just copy paste the original problem. There is no question about the validity of the solution. My question is about the statement in the solution "Consider the instant when the mass is moving vertically upward. In this instant the...

I have been reading Manton & Sutcliffe for some time now and can't quite wrap my head around something. If you take the Hopf invariant N of a topological soliton ϕ then its Skyrme-Faddeev energy (which I hope I've gotten right up to some constants) E=∫∂iϕ⋅∂iϕ+(∂iϕ×∂jϕ)⋅(∂iϕ×∂jϕ) d3x satisfies...

Hey there, I've been recently been going back over the basics of GR, differential geometry in particular. I was watching one of Susskind's lectures and did not understand the argument made here (26:33 - 35:40). In short, the argument goes as follows (I think): we have some generic metric ##{ g...

Hello there, I had another similar post, where asking for proof for Hilbert’s Hotel. After rethinking this topic, I want to show you a new example. It tries to show why that the sentence, every guest moves into the next room, hides the fact, that we don’t understand what will happen in this...

The attached image shows the text I am following. I get that the 3-D pdf F can only depend on the speed v. I also understand that if f_x , f_y, f_z are the pdfs of the individual components of velocity, then rotational invariance requires them to all be the same function f_x = f_y = f_z = ϕ...

I would be interested in what people think of Fulvio Melia's new cosmological paper in which he argues that the comoving frame is locally inertial only if we have a linearly expanding Universe (or Minkowski spacetime)...

above video states that arg(z1/z2) = arg(z1) - arg(z2) this is seems very similar to Log rules but these are inverse function for angles right? And log rules only apply to logarithms, not sure where he got this from? What am i missing?

Hi, This is on the wikipedia entry for the Euler Lagrange equation. Here is a link. https://en.wikipedia.org/wiki/Calculus_of_variations#Euler%E2%80%93Lagrange_equation The notation I am confused about is this: Aren't the y(x) and the y'(x) unnecessary to list as arguments when x is...

I came across a question recently which involved calculating the change in wavelength of a photon between being emitted from the surface of the sun and arriving at the Earth. The method that was implied involved calculating the GPE's of the photon (assuming the photon to have a mass h/[c...

In chapter 44 of Feynman Lectures on Physics, Volume I, which covers thermodynamics, we find this passage: Does anyone know what this argument of Carnot's is? I'm not sure exactly what it is that he is supposed to have derived without using the first law. The efficiency of a reversible...

Hi. If I have a function f(x) = √(x+1) and I define u=x+1 is it correct to state f(u) = √u ?

Problem Statement: What is the correct way of computing the argument of the following equation? Relevant Equations: I am trying to compute the argument ##\Phi## of the equation $$\frac{r-\tau\exp\left(i\varphi\right)}{1-\tau r\exp\left(i\varphi\right)} \tag{1}$$ which using Euler's equation...

Show that the value of ##\int_0^1\sqrt(1-cosx)dx## is less than or equal to ##\sqrt2## ##1\ge cos x\ge-1## The problem is a worked one but I am just confused by a simple thing. We integrate the function f ##\int_0^1\sqrt(1-cosx)dx in the interval [0,1] but I don't understand that what stands...

"In 1961, physicist Robert H. Dicke claimed that certain forces in physics, such as gravity and electromagnetism, must be perfectly fine-tuned for life to exist anywhere in the universe. Fred Hoyle also argued for a fine-tuned universe in his 1984 book Intelligent Universe. Much as been written...

Homework Statement Find ##\iint_S ydS##, where ##s## is the part of the cone ##z = \sqrt{2(x^2 + y^2)}## that lies below the plane ##z = 1 + y## Homework EquationsThe Attempt at a Solution [/B] I have already posted this question on MSE...

Hi. If I have a function for example f( x ) = x2 + x then to obtain f( -x) I just put (-x) in place of the x in f(x) so I get f( -x) = x2 - x Am I right so far ? So f(x) and f(-x) look like different functions but if you put a negative number in f(-x) it flips the -x back to +x so are f(x) and...

Homework Statement The indefinite integral $$\int \, $$ and it's argument. The indefinite integral has a function of e.g ## \cos (x^2) \ ## or ## \ e^{tan (x)} \ ## If the argument of ## \cos (x^2) \ ## is ## \ x^2 \ ## then the argument of ## \ e^{tan(x)} \ ## is ## \ x \ ## or ## \ tan (x) \...

I'm trying to go through chapter III of the vol.8 of Landau and Lifshitz series. (Fortunately the book is uploaded to the archive.org, I guess it is in the public domain.) At page 87 ( << Archive.org link deleted by the Mentors because of copyright violation >> ), they speak about the Joule...

In plasma physics we have what is known as plasma dispersion function. There are two approximation under which this function can be expanded: when the argument is less than 1, we can use power series expansion and when the argument is greater than 1 we can have asymptotic expression. My...