What is Complex: Definition and 1000 Discussions

The UCL Faculty of Mathematical and Physical Sciences is one of the 11 constituent faculties of University College London (UCL). The Faculty, the UCL Faculty of Engineering Sciences and the UCL Faculty of the Built Envirornment (The Bartlett) together form the UCL School of the Built Environment, Engineering and Mathematical and Physical Sciences.

View More On Wikipedia.org
Recent contents Top users
  1. N

    Forced Oscillation with complex numbers

    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...
  2. E

    Why Complex Scalars in 4D Supersymmetric Theories?

    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?
  3. LarryS

    Complex numbers sometimes *Required* in Classical Physics?

    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...
  4. astrololo

    Finding polar form of complex number

    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...
  5. C

    Derivation of momentum for the complex scalar field

    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) +...
  6. V

    Complex number equality problem

    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...
  7. C

    How to Solve Equations with Complex Numbers

    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...
  8. Vinay080

    Motivation for geometrical representation of Complex numbers

    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...
  9. terryds

    Rationalizing complex root

    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...
  10. W

    C_0 coefficient of Complex Fourier transforms

    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}}...
  11. X

    Best way to solve a system of complex equations?

    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...
  12. T

    Deciding between group theory vs. complex analysis

    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...
  13. Y

    Complex Covariance: Analyzing X & Y Relationships

    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...
  14. thegirl

    Method used to find harmonic functions in complex analysis

    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...
  15. Billmyk

    Superpositions and complex structures

    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...
  16. Indianspirit

    Why does the complex conjugate of psi pop out?

    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...
  17. L

    Complex Integrals, Antiderivatives, Logarithms

    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)...
  18. astrololo

    Solving a polynomial with complex coefficients

    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 ?
  19. astrololo

    Proof of Complex Conjugates and Real Coefficients | Complex Numbers Homework

    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...
  20. R

    Finding complex power in AC circuit

    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...
  21. Einstein's Cat

    Exploring Effects of Multiplying Kets by Complex Numbers

    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...
  22. Steve Turchin

    Complex absolute value inequality

    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| \\...
  23. K

    Understanding Qubits and Complex Scalars: The Role of Imaginary Numbers

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

    Complex numbers and physical meaning

    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...
  25. astrololo

    Calculating the roots of a quadratic with complex coefficien

    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...
  26. Den Webi

    A link from complex number to hypercomplex numbers

    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...
  27. C

    Complex Degree of Coherence (Cittert-Zernike)

    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...
  28. Rectifier

    Complex currents and voltages - current in a branch

    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 =...
  29. S

    Integration of complex exponentials

    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}|)\...
  30. icesalmon

    Does Shifting Time Reference in AC Circuits Help Simplify Functions?

    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°) =...
  31. H

    Fortran Solving Fortran Runtime Error 112 - Mach Number Calculation

    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...
  32. N

    MATLAB Plotting Complex Wavefunction - Matlab

    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...
  33. G

    Cloud Computing for Complex Scientific Computations - Free Trial Available!

    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...
  34. astrololo

    Why do we need the set of complex numbers to solve?

    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.
  35. P

    Please give some hints on the Complex projective group

    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...
  36. D

    Complex numbers and polynomial

    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...
  37. Calpalned

    Physical applications of complex numbers

    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...
  38. Calpalned

    A question about complex numbers

    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##
  39. LunaFly

    Why is Fourier Transform of a Real Function Complex?

    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...
  40. R

    How to communicate 3d CAD with complex surfacing?

    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...
  41. D

    Real integral=area , complex integral= ?

    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 ?
  42. RJLiberator

    Simple proof of Complex Inner Product Space

    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>...
  43. T

    Physics of Complex Systems Vs Plasma Physics/Nuclear Fusion?

    Thank you for opening my first thread. I have just began studying Physics at a university in Hungary and would like to get some information about Physics of Complex Systems and Plasma Phyics/Nuclear Fusion. In my life, finding a goal have always helped me work harder and focus on my studies...
  44. A

    MHB What is the complex number C for the transformation T?

    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...
  45. O

    Refraction and Snell's Law, A complex question

    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.
  46. RJLiberator

    Simple Complex Vector Space Proof Clarification

    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...
  47. wirefree

    Understanding Complex Exponential Summation: How is the Arctan Function Used?

    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
  48. S

    Simplifying natural log of complex number

    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...
  49. L

    Complex numbers - I'm sure this is an easy - Argand diagram

    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...
  50. T

    Complex integral for z-transform causality

    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...
Back
Top