Complex Definition and 1000 Threads

Homework Statement Of all complex numbers that fit requirement: ## |z-25i| \leq 15## find the one with the lowest argument. Homework EquationsThe Attempt at a Solution z=a + ib (a, b are real numbers) ## \sqrt{a^2 + (b-25)^2} \leq 15 \\ a^2 + (b-25)^2 \leq 225 ## The lowest possible...

Homework Statement Given n=(x + iy)/2½L and n*=(x - iy)/2½L Show that ∂/∂n = L(∂/∂x - i ∂/∂y)/2½ and ∂/∂n = L(∂/∂x + i ∂/∂y)/2½ Homework Equations ∂n Ξ ∂/∂n, ∂x Ξ ∂/∂x, as well as y. The Attempt at a Solution ∂n=(∂x + i ∂y)/2½L Apply complex conjugate on right side, ∂n=[(∂x + i ∂y)/2½L] *...

Homework Statement Solve the following equation: ## (1+a)^n=(1-a)^n## where a is complex number and n is natural number Homework Equations Euler's formula The Attempt at a Solution I've tried something like this ## (1+a)^n=(1-a)^n \\ (\frac{1+a}{1-a})^n=1 ## But i really have no idea...

hello! 1) what is the process to get the derivative of an equation that requires you to do first the chain rule and then the product/quotient rule, eg. sin(x^2(x+1))? 2) what is the process to get the derivative of an equation that requires you to do first the product/quotient rule and then the...

Homework Statement Suppose that the characteristic equation to a second order, linear, homogeneous differential equation with constant coefficients yielded two complex roots: \begin{array}{l} {\lambda _1} = a + bi\\ {\lambda _2} = a - bi \end{array} This would yield a general solution of: y =...

Homework Statement I've been asked to graphically verify that the system of equations F (that I've uploaded) has exactly 4 roots. And so I did, using the ContourPlot function in Mathematica and also calculated them using FindRoot. Now, I've to approximate the zeros of F using the fixed point...

Homework Statement It is known that roots of complex polynomial: ##P_n (z) = z^n + a_{n-1}z^{n-1} + \cdots + a_1z + a_0## are the following complex numbers: ##\alpha_1, \alpha_2, \cdots, \alpha_n ## Find the product: ##\prod = (\alpha_1 + 1)(\alpha_2 + 1)\cdots(\alpha_n +1)## Homework...

I tried my best but I wasn't able to solve this can someone please provide me with a detailed solution. Here 's the question : Establish the expression of Vs/Ve (complex) using Thevnin's theorem Here is the circuit : I spent 4 hours trying to solve this but I had no clue how. I'am having...

Homework Statement [/B] Find and classify all singularities for (e-z) / [(z3) ((z2) + 1)] Homework EquationsThe Attempt at a Solution [/B] This is my first attempt at these questions and have only been given very basic examples, but here's my best go: I see we have singularities at 0 and i...

I am looking for conformal transformations to map: 1. Disk of radius R to equilateral triangular region with side A. 2. Disk of radius R to rectangular region with length L and width W. 3. Disk of radius R to elliptic disk with semi-major axis a and semi-minor axis b. Thanks!

Homework Statement If a force F = F_0 cos (\omega t) = \Re{\{F_0 e^{i \omega t}\}} is applied to a body of mass m attached to a spring of constant k, and x = \Re\{z\} . Show that the following equation holds: m \ddot{z} = - k z + Fe^{i \omega t} . Homework Equations Newton's second law. The...

The scalar fields of supersymmetric theories in 4 spacetime dimensions are a set of complex fields (usually denoted by ##z^{\alpha}##). How can this be physically translated? More precisely, we know that in 5D, those scalars are real, so what is that makes them real here but complex there?

In general, one thinks of complex numbers as being absolutely required in Quantum Physics but as being optional in Classical Physics. But what about modern classical electromagnetic field theory (gauge theory) in which the electromagnetic field is coupled to the field of charged particles by...

Homework Statement I have the following complex numbers : -3,18 +4,19i I must put it in polar form. Homework Equations r=(a^2+b^2)^(1/2) cos x = a/r sin x = b/r The Attempt at a Solution I was able to find with cos x = a/r that the x = 127,20 But when I do it with sin x = b/r I obtain like...

The conserved 4-momentum operator for the complex scalar field ##\psi = \frac{1}{\sqrt{2}}(\psi_1 + i\psi_2)## is given in terms of the mode operators in ##\psi## and ##\psi^{\dagger}## as $$P^{\nu} = \int \frac{d^3 p}{(2\pi)^3 }\frac{1}{2 \omega(p)} p^{\nu} (a^{\dagger}(p) a(p) +...

Homework Statement The problem states that you need to solve the following equation (without a calculator) : z^5 = z̅ Homework Equations z=a+bi and z̅=a-bi The Attempt at a Solution So far I've tried multiplying both sides by z̅: z̅ * z^5 = |z̅|^2...

I have to solve the following equation: z4=i*(z-2i)4 Now, i tried to move everything but i (imaginary number) to the left side and then find the 4-th root of i, when i did that, i had four solutions, with one of them being eiπ/8. But i don't know what to do with the left side, since i get way...

I am seeing in "slow motion" the development of vectorial system. I am reading the book "A History of Vector Analysis" (by Michael J.Crowe); it seems from my acquaintance that the vector concept came from the quaternions concept; and the quaternions concept came from the act of search for...

Homework Statement If ##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=a+b\sqrt{6}##, then a+b is ? A) 8 B) 7 C) 6 D) 5 E) 4 The Attempt at a Solution [/B] This is my attempt...

Mod note: Moved from technical math section, so no template was used. Hey! So the complex Fourier transform of the square wave $$ f(x) = \begin{cases} 2 & x \in [0,2] \\ -1 & x \in [2,3] \\ \end{cases}, \space \space f(x+3) = f(x)$$ is ##C_k = \frac{3j}{2 \pi k}( e^{-j \frac{4 \pi k}{3}}...

In my circuit analysis class I consistently need to solve system of complex equations, and I can't use MATLAB or anything for it. Suppose I have the following system: (Va-Vs)/(-j15) + Va/33 + (Va-Vo)/(-j25)=0 (Vo-Va)/(-j25) + (Vo-Vs)/10 = 0 What is the best way to solve it by hand in a time...

Hi, I have one spot remaining to take a pure math course, and I'm trying to decide between complex analysis and group theory. Although I've touched some of the basic of dealing with complex numbers in my physics/DE courses, they haven't gone in much depth into them beyond applications. On the...

Apologies for misleading title 1) Let's say I have some process e.g. an gravitational orbit or something that results in x = sin(w t) and y = cos (w t) 2) a. Clearly x and y are related, but using a simple correlation <x|y>/(<x^2><y^2>)**0.5 will result in 0. That is, x and y are not...

Hi, I was just wondering how would you go about finding a harmonic function in complex analysis when given certain conditions such as I am z > 0 and is 1 when x > 0 and 0 when x < 0. Do you draw a diagram? Do you solve the laplace equation? How would you go about doing this? What if there...

So I get that when starting at Eigenstate A all super-positions wave functions are collapsed do to entanglement with "observed eigenstate A. My theoretical question is since sub-atomic particles are entangled in there "eigenstate" space-time positions, wouldn't that mean that complex structures...

I just started teaching myself multivariable calculus and I know what the modulus of a complex number is but what is the complex conjugate and why does it pop out when we take the mod square of psi? Like the first minute or two of video... What are complex conjugates, how does one find them...

I've been teaching myself a little bit of Complex Variables this semester, and I had a question concerning complex integrals. If I understand correctly, then if a function f has an antiderivative F , then the line integral \int_C f(z) dz is path independent and always evaluates to F(z_1)...

Homework Statement z^6+(2i-1)z^3-1-i=0 Homework EquationsThe Attempt at a Solution I know that I must put k=z^3 and solve the quadratic. But I'm not able to simplify the quadratic. I get the square root of (-8i+1) What am I supposed to do ?

Homework Statement I have two complex numbers that are non real, k and z. K and z are going to be complex conjugates if and only if the product (x-k)(x-z) is a polynomial with real coefficients. Here is my answer : k=a+bi z=c+di (x-k)(x-z) = x^2 -(k+z)x+kz Homework EquationsThe Attempt at...

In a branch I have to find complex power which is having current 19.41<-37.3 A and impedance 4+j3 Ω What I used is i2z and I was getting 1489.85 - j1152.74 W. This is wrong but I don't know how because by this site the answer was different...

In Dirac's "The Principles of Quantum Mechanics," ket vectors are multipled by complex numbers (c1 |A> + c2 |A> = c1 + c2 |A>) and I was curious what affect this has a) on the ket vector and b) on the entire system? Also is (c1 |A> + c2 |A> = c1 + c2 |A>) equal to (|A> + |A> = |A>)? Thank you...

Solve the following inequality. Represent your answer graphically: ## |z-1| + |z-5| < 4 ## Homework Equations ## z = a + bi \\ |x+y| \leq |x| + |y| ## Triangle inequality The Attempt at a Solution ## |z-1| + |z-5| < 4 \\ \\ x = z-1 \ \ , \ \ y = z-5 \\ \\ |z-1+z-5| \leq |z-1| + |z-5| \\...

Hi, Does anybody know why we have complex scalers to represent qubits..I mean why they are not real numbers. Thanks

I have to say that I am a bit confused with the use of complex numbers. I know that: 1. They have been created by mathematicians to solve the "real"ly unsolved equation of x^2=-1. 2. They are used in many aspects of physics, like waves and quantum theory, with terrific correspondence to the...

Homework Statement Calculating the roots of a quadratic with complex coefficients Homework Equations x^2 - (5i+14)x+2(5i+12)=0 The Attempt at a Solution I tried the quadratic solution but it gives too complicated solutions. I have no idea on how to do this...

If i understand correctly, the discovery of complex numbers was linked to solving real number problems, s.a. finding square roots of negative numbers. In other words, at first there was a problem that was formulated using real numbers only that had no real number solutions, which lead to...

Homework Statement A light source consists of two long thin parallel wires, separated by a distance, W. A current is passed through the wires so that they emit light thermally. A filter is placed in front of the wires to only allow a narrow spectral range, centred at λ to propagate to a...

The problem I want to calculate ## |I_1| ## The attempt ## V_m = Z_{total}I_1 \\ I_1 = \frac{V_m}{Z_{total}} ## ## Z_{total} = \frac{ \frac{1}{jwC }\cdot (R + jwL) }{\frac{1}{jwC} + R + jwL} \\ \frac{ R + jwL }{1 + jwCR + jwCjwL} \\ \frac{ R + jwL }{1 - w^2LC + jwCR } \\ ## ## I_1 =...

I am trying to understand how to go from the first line to the next: ##\frac{1}{(2\pi)^{3}}\int d^{3}p\ e^{-it\sqrt{{\bf{p}}^{2}+m^{2}}}\ e^{i {\bf{p}}({\bf{x}}-{\bf{x}}_{0})} = \frac{1}{2\pi^{2}|{\bf{x}}-{\bf{x}}_{0}|} \int_{0}^{\infty} dp\ p\ sin(p|{\bf{x}}-{\bf{x}}_{0}|)\...

In class we've been talking about circuits with AC sources of the form v(t) = Vmcos(ωt+θ) which produces a current i(t) = Imcos(ωt+Φ). They go on to talk about shifting their time reference by re-writing the function for voltage, Vmcos(ωt + θ - 90°) = Vmsin(ωt+θ) the current Imcos(ωt+Φ-90°) =...

Hi, I try to write program to calculating mach number, with using bisection method. When I run program, fortran write to me an error in line 40. Can you help? I tried to calculating function by using wolfram sucesfully but I need to run it on fortran, An equation is 1.7795 - (0.334898 (1 + 0.2...

Hi, I am wondering how to plot a complex function of the form: Ψ(t) = Ansin(n⋅pi⋅x/L)e-iEnt/h + Bnsin(m⋅pi⋅x/L)e-iEmt/h + ... + where m and n are known eigenvalues of the infinite square well with corresponding energy En, for any particular x? So, this will be a function of solely t. Any help...

Hi. I am doing some complex computations using c, c++, matlab, python. It is very slow on a conventional PC. I heard, there is a way to do scientific computations remotely. Such that I could sort of get an access to the remote advanced PC, and perform computation remotely there. And then...

I was wondering, why is the set of complex numbers needed to solve problems that the set of reals doesn't permit to ? I mean, in relation to the fundamental theorem of algebra, that is.

The O(N) nonlinear sigma model has topological solitons only when N=3 in the planar geometry. There exists a generalization of the O(3) sigma model so that the new model possesses topological solitons for arbitrary N in the planar geometry. It is the CP^{N-1} sigma model,†whose group manifold is...

Homework Statement Hi,I have a problem regarding to one of the questions in my homework.Actually I am not trying to ask for the solution.I am just not sure what the question is asking for.Please see the attachedHomework EquationsThe Attempt at a Solution In 5(c),the summation notation stated...

Homework Statement Homework Equations see picture above The Attempt at a Solution I can follow most of the steps, but not all. I got confused with finding ##|\frac{dz}{dt}|##. It is easy to derive ##\frac{dz}{dt}## from ##z##. Normally, I would square the two components of ##dz/dt## and...

Homework Statement I don't understand example 2. For part a, I got a slightly different answer. Homework Equations see picture The Attempt at a Solution ##|z-1|=2=\sqrt{x^2+y^2-1}## ##4=x^2+y^2-1 \neq (x-1)^2+y^2##

Homework Statement Find the Fourier transform F(w) of the function f(x) = [e-2x (x>0), 0 (x ≤ 0)]. Plot approximate curves using CAS by replacing infinite limit with finite limit. Homework Equations F(w) = 1/√(2π)*∫ f(x)*e-iwxdx, with limits of integration (-∞,∞). The Attempt at a Solution I...

Hello everyone I am sure the answer to this would be on the internet but I can't seem to find much. When we create a complex 3d cad (examples include Aerodynamic Helmet of a cycle biker, computer mouse, exhaust fan blades etc) that includes complex surfacing in cad, how does one communicate...