Complex Definition and 1000 Threads

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...

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...

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...

Hi. If a real integral between 2 values gives the area under that curve between those 2 values what does a complex integral give between 2 values ?

Homework Statement Prove that <v|0>=0 for all |v> ∈ V. Homework EquationsThe Attempt at a Solution This is a general inner product space. I break it up into 2 cases. Case 1: If |v> = 0, the proof is trivial due to inner space axiom stating <0|0> = 0. Case 2: If |v> =/= 0 then: I use <v|0>...

The transformation T maps the plane onto itself by multiplication by a complex number. That is, there is a complex number C=a+ib such that for any point P(x,y), T(P) is the point corresponding to the complex number C⋅P. For a particular complex number C the transformation T takes the smaller...

Homework Statement Calculating the refraction of index (n) with given information. Homework Equations The Attempt at a Solution I tried to use Snell's Law but I have no idea about how I'm supposed to use it without angles. Instead, question gives distances. Need help very badly.

Homework Statement Let v ∈ V and c ∈ ℂ, with c ≠ 0. Prove that if cv = 0, then v = 0. Homework Equations Vector space axioms. The Attempt at a Solution Simple proof overall, but I have one major clarification question. v = 1v = (c^(-1)c)v = c^(-1) (cv) = c^(-1) 0 v = 0 My question is, in...

I appreciate the opportunity afforded by this forum to submit a question. I have struggled with the derivation shown in the attached picture. I am certainly unfamiliar with the concept used to include the arctan function in the encircled step. Would be highly appreciative of a prompt.wirefree

Homework Statement The problem is to sketch lines of constant u and v in the image plane for the function Log[(z+1)/(z-1)]. Homework Equations z=x+iy The Attempt at a Solution In order to do this I have to get the expression into u+iv form, so that I can read off and manipulate the u and v...

Homework Statement OABC is a square on an Argand diagram. O Represents 0, A represents -4 + 2i, B Represents z, C represents w and D is the point where the diagonals of the square meet. (There are two possible squares that meet this criteria) Find the complex number represented by C and D in...

This relates to z-transform causality, but I'll try to phrase it as a complex analysis question. Suppose I have a function ##X(z)## whose poles are all inside the unit circle, and which has the property \lim_{|z|\to\infty} \frac{X(z)}{z} = 0 Is that sufficient to guarantee that \frac{1}{2\pi...

As an undergraduate, which graduate-level course will prepare me better for grad school, Complex Analysis or Topology? I probably can't fit both into my schedule, but I can definitely fit one. I have already taken undergraduate complex analysis and I'm taking now undergraduate topology. My...

Hi everyone, Can you please assist with the following problem? The complex numbers z and w are such that for the real variable x, (x-z)(x-w)=ax2+bx+c for real a,b and c. By letting z=p+qi and w=r+si, prove that z and w must be conjugates of one another.So far, I have determined that a=1...

I know this is probably the least of my worries at the moment but my quantum textbook solves ##\frac{\mathrm{d}\phi (t) }{\mathrm{d} t}=\frac{iC}{h}\phi (t) ## as ##\phi (t) = e^{-i(\frac{C}{h})t}##. Is this not off by a sign? Its really bugging me.

Homework Statement A rope is wrapped through an angle θ about a horizontal pole (So for ex- ample, θ = 2π would imply the rope goes around one full time). The rope and the pole have a static friction coeffecient of μ, and the pole is of radius r. From one end of the rope hangs a mass m. How...

Attached image with problem. 2 Questions; 1. δn.|AB| = δx.|BC|.cosΘ becomes δn = δx.|BC|.cosΘ / |AB| This is dividing the entire "δx.|BC|.cosΘ" equation by |AB| or just the |BC| part? Is there a difference? 2. Half way down page, boxed equation. How does δx.|BC|.cosΘ / |AB| = δxcos^2Θ and...

Homework Statement I need to find the complex angle θ for: 2√(3)-2i in polar form. Homework EquationsThe Attempt at a Solution If I draw a complex plane, I can see that 2√3 on the real axis gives 0°, and -2i gives 3π/2 (270°), but it's incorrect. How can I find the complex angle of 2√(3)-2i...

(1+a)n = (1-a)n I tried following: (1+a)n = (1-a)n [(1+a)/(1-a)]n=1 but what can i do next?

Homework Statement Describe all the singularities of the function ##g(z)=\frac{z}{1-\cos{z}}## inside ##C## and calculate the integral ## \int_C \frac{z}{1-\cos{z}}dz, ## where ##C=\{z:|z|=1\}## and positively oriented. Homework Equations [/B] Residue theorem: Let C be a simple closed...

Homework Statement Let ##D={z : |z| <1}##. How many zeros (counted according to multiplicty) does the function ##f(z)=2z^4-2z^3+2z^2-2z+9## have in ##D##? Prove that you answer is correct. Homework Equations 3. The Attempt at a Solution [/B] The function has no zeros in ##D##, which can be...