# Ppt on argand plane

##### ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY.

resistor and capacitor in parallel Cole-Cole Plots: Impedance Plots in the Complex Plane When we plot the real and imaginary components of impedance in the complex plane (Argand diagram), we obtain a semicircle or partial semicircle for each parallel RC Voigt/grains, grain boundaries, and electrodes can be seen more distinctly. The complex impedance data can be displayed in the complex impedance plane with real part  as the abscissa and the imaginary part  “ as the ordinate (Cole Cole diagram). A typical /

##### Numbers: Real, Imaginary, Complex, and Beyond... Roger House Scientific Buzz Café Coffee Catz Sebastopol, CA 2010 February 3 Copyright © 2010 Roger House.

numbers, so is 2-dimension- al, as was noted by: Caspar Wessel (1745-1818) Jean Robert Argand (1768-1822) Carl Friedrich Gauss (1777-1764) 48 The complex plane -2 -1 0 1 2 i i -i 2i -2i 2+i 2-i 49 is algebraically closed/. In some sense they arent even related, except, perhaps, historically. 52 Three is better than two? Complex numbers and the complex plane proved to be extremely powerful tools for creating precise mathematical models in two dimensions. A natural question: What about a number system for /

##### MM3FC Mathematical Modeling 3 LECTURE 7 Times Weeks 7,8 & 9. Lectures : Mon,Tues,Wed 10-11am, Rm.1439 Tutorials : Thurs, 10am, Rm. ULT. Clinics : Fri,

on, I shall use H(e -j  ) in place of H(  ) to emphasise the connection between the  -domian and the z-domain. … (7.3) The z-Plane & the Unit Circle The frequency response is periodic with period 2 . Thus, we only need evaluate it over (-  <  <  ). Thus, the values of z = e -/2 | arg(z 2 ) z2z2 z 3 = z 2 * We display all of this on a ‘Pole-Zero Plot’. (This is just an Argand diagram with a unit circle on and the poles and zeros displayed in the following way). Imag Real X 3 O O O pole zero A pole is /

, b) in a rectangular coordinate system. When a rectangular coordinate system is used to represent complex numbers, the plane is called the complex plane or the Argand plane. The x- axis is also called the real axis, because the real part of a complex number is plotted/Slide 7.5 - 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1 Plotting Complex Nubmers Plot each number in the complex plane. A: 1 + 3i B: –2 + 2i C: –3 D: –2i E: 3 – i Solution Slide 7.5 - 7 Copyright ©/

##### Point Velocity Measurements

past any unknown object can be represented as a complex potential. In particular we define the complex potential In the complex (Argand-Gauss) plane every point is associated with a complex number In general we can then write Now, if the function f is analytic, /that it is also differentiable, meaning that the limit so that the derivative of the complex potential W in the complex z plane gives the complex conjugate of the velocity. Thus, knowledge of the complex potential as a complex function of z leads to /

##### Electrochemistry MAE-295

Impedance Vector Impedance  ‘resistance’ Admittance  ‘conductance’: Representation of impedance value, Z = a +jb, in the complex plane (see also http://math.tutorvista.com/number-system/absolute-value-of-a-complex-number.html Data Presentation: Nyquist Plot with Impedance / Nyquist Plot with Impedance Vector When we plot the real and imaginary components of impedance in the complex plane (Argand diagram), we obtain a semicircle or partial semicircle for each parallel RC Voigt network: Nyquist plot or also/

##### B Lifetime and Oscillation Results from CDF and D0 Andrzej Zieminski Indiana University (for the D0 and CDF Collaborations) HCP 2004 East Lansing, June.

 1 ) cos(  2 ) exp(-i  1 ) A ┴ = sin(  1 ) sin(  2 ) exp(-i  2 ) Transversity plane in the J/  rest frame B meson defines positive x-axis K  (KK) plane defines (x,y) plane K (K + ) +ve y momentum  T,  T polar & azimuthal angles of  +  K helicity angle of K* (  ) 15 /-0.09±0.13±0.06 This measurem.0.63 ±0.04 ±0.030.18 ±0.05 ±0.053.07 ±0.40 ±0.070.11±0.23±0.06 17 Argand Diagrams dominant longitudinal polarization  L /  = |A 0 | 2 non-zero parity-odd fraction  ┴  = |A ┴ | 2, (P-wave, CP= -1 /

##### Experiments on Biological Structure - Optical Microscopy - Electron Microscopy - X-ray crystallography - NMR Spectroscopy - Fluorescence Spectroscopy.

= 2  r. ( s - s 0 ) = 2  r.S | s 0 |=| s |=1/ |S|=2sinθ/λ Diffraction Scattering by a crystal – Braggs law: diffraction as reflection from crystal planes d   path difference = 2dsin θ For constructive interference, nλ = 2dsinθ | S | = 2sin  /  = 1/d If a diffraction pattern fades out at an angle of 2  / vectors are pointing in different directions. t=0 t=1 2  i t a. S t=2 t=3 t=4 t=5 t=6 Argand diagramm Laue Conditions: a.S = h b.S = k c.S = l h, k, l are whole numbers either zero, positive or /

##### Copyright R. Janow – Fall 2015 Physics 121 - Electricity and Magnetism Lecture 14-15_E - AC Circuits, Resonance Y&F Chapter 31, Sec. 3 – 8, No Y&F reference.

form: Addition: Copyright R. Janow – Fall 2015 Representation using the Complex Plane Imaginary axis (y) Real axis (x) x y |z|  Magnitude 2 : Polar form: Argument: “Argand diagram” Picture also displays complex-valued functions Copyright R. Janow – Fall 2015/ Re    Let a(t) be a sinusoidally varying real quantity to be pictured as a vector in the complex plane rotating (counterclockwise) at angular frequency  Copyright R. Janow – Fall 2015 Complex exponentials (time domain phasors) are solutions of /

##### F. Martínez-Vidal IFIC – Universitat de València-CSIC Measurement of the CKM-matrix angle  (  3 ) (at B Factories) Outline Introduction: CKM, UT and.

, isolated resonance For broad, overlapping and many channel resonances we need a more general approach  K-matrix formalism (Argand diagram) Int. WE Heraeus Summer School, September 2 nd, 2005 F. Martínez-Vidal, Measurements of the CKM/shapes of selection variables (mES, DE, Fisher, etc.) –Background fractions and Dalitz shapes –Efficiency variations across Dalitz plane (including tracking efficiency) –Invariant mass resolution –Biases from control samples Dalitz model systematic uncertainty includes: –No /

##### ITEP-PNPI Spin Rotation Parameters Measurements and Their Influence on Partial Wave Analyses. I.G. Alekseev, P.E. Budkovsky, V.P. Kanavets, L.I. Koroleva,

amplitude, not changing the values of differential cossection and asymmetry while affecting A and R.  In the w-plane such transformation is equivalent to mirroring of a trajectory across the unit circle  crossing points are critical for branching / constatnt or linearly varying background M  resonance mass   full width R=  EL / 2   resonance circle radius on Argand plot   pole residue phase B  background parameters  Pole parameters for all 7  -isobars in the second resonance region were /

##### Copyright R. Janow – Fall 2015 Physics 121 - Electricity and Magnetism Lecture 15E - AC Circuits & Resonance II No Y&F reference for slides on Complex.

PART Copyright R. Janow – Fall 2015 Representation using the Complex Plane Imaginary axis (y) Real axis (x) x y |z|  Magnitude 2 : Polar form: Argument: “Argand diagram” Picture also displays complex-valued functions Copyright R. Janow –/” A (often simply called a “phasor”): Represent sinusoidally varying real quantity a(t) as a vector in the complex plane, rotating (counterclockwise) at angular frequency  Copyright R. Janow – Fall 2015 Phasor Definitions, continued A phasor represents a sinusoidal/

##### Mathematics to Innovate Blade Profile P M V Subbarao Professor Mechanical Engineering Department Also a Fluid Device, Which abridged the Globe into Global.

Flow field can be represented as a complex potential. In particular we define the complex potential In the complex (Argand-Gauss) plane every point is associated with a complex number In general we can then write The Cauchy-Riemann conditions are: Differentiating/as a complex function of z leads to the velocity field through a simple derivative. Fertile Complex Potentials ELEMENTARY IRROTATIONAL PLANE FLOWS The uniform flow The source and the sink The vortex Creation of mass & Momentum in Space by Nature THE/

##### Complex Numbers Adding in the Imaginary i By Lucas Wagner.

the sum of a real and imaginary part maintains a good algebraic field. For example, Complex Numbers as Vectors Jean-Robert Argand in 1806 came up with the idea of a geometrical interpretation of complex numbers. Replace the x-axis with the real / the vector, and e iθ gives the direction. Physics Application: Centripetal Motion Create a parametrization of the position in the complex plane, Consider an object moving in a circle of radius r with an angular frequency of ω. What is its velocity and acceleration?/

##### A. Introduction Are We Speaking the Same Language? 1. Why this interests me. 2. Where do definitions come from? 3. Math Dictionaries related to this discussion.

one of which real numbers are represented, and on the other pure imaginaries, thus providing a reference for graphing complex numbers. Argand diagram E. Some unusual mathematical terms Are We Speaking the Same Language? Perfect number: A number equal to the sum of all/? Quadrinomial: a four-term polynomial. I propose the following new definitions: Axial points: Points on an axis. In the x-y-plane, an axial point is any point that has at least one 0 coordinate. Betweenness inequality: a < x < b. This means /

##### Multiwavelength Anomalous Dispersion, Density modification, Molecular replacement, etc. Protein Structure Determination Lecture 9.

Phase probability distribution Radii are F p and k*F ph Width are  p and k*  ph The red area are the places in Argand space where both F P and F PH -F H can be Most probable versus best phase The most probable phase is not necessarily the “best/ centric, maving phase = 0° or 180° If the crystal has 2-fold, 4-fold or 6-fold rotational symmetry, then the reflections in the 0-plane are centric. (Because the projection of the density is centrosymmetric) For centric reflections: |F ph | = |F p | ± |F h | This /

##### March 10, 2016Introduction1 Important Notations. March 10, 2016Introduction2 Notations.

general The conjugate Complex Conjugate Phasor = Rotating Arrow + Associated Phase AnglePhasor Representation of a complex number in terms of real and imaginary components Im Complex Plane r sin  r cos  Re z  ^ Argand/Phasor Diagram © SPK Complex Plane Taylor series is a series expansion of a function about a pointseries expansionfunction 1-d Taylor series expansion of a real function about a point/

##### March 19, 2016Introduction1 Important Notations. March 19, 2016Introduction2 Notations.

general The conjugate Complex Conjugate Phasor = Rotating Arrow + Associated Phase AnglePhasor Representation of a complex number in terms of real and imaginary components Im Complex Plane r sin  r cos  Re z  ^ Argand/Phasor Diagram © SPK Complex Plane Consider the following Maclaurin series expansions Expansions are valid for complex arguments x too Function : Complex Numbers & Simple Harmonic Oscillations March 19, 2016March 19, 2016March/

##### Complex numbers.

the vector by -1 and it points the other way i.e. a 180° shift As -1 = j2 then j lies between them i.e. a 90° shift Complex plane or argand diagram j -c+jd Imaginary a+jb j2= -1 Real g-jh -e-jf j3=-j Polar form of a complex number The number may be represented by its vector/

##### 2.4 Complex Numbers What is an imaginary number What is a complex number How to add complex numbers How to subtract complex numbers How to multiply complex.

(rationalizing the denominator) For some reason we dont like is in the denominator. So we rewrite the fraction by multiplying by the complex conjugate. Example Plotting Complex Numbers (on the Argand plane) i R -5 – 2 i 2 – 2 i 2 + 3 i -5 -2 + 3 i -3 i

##### Chp3 MATLAB Functions: Part1

DIVISOR divided by itself z2 z1 = (x22 + y22) z2 z2* z1z2* x1 x2 + y1 y2 + j y1 x2 – x1 y2 Division Complex No.s – Graphically The Argand diagram Modulus (magnitude) of z r = mod z = |z| = x2 + y2 x y r  z = x + i y Im(z) Re(z) Argument (/ Euler Identity Where Then from the Vector Plot Need to be careful abaout the values of θ when z is in the LEFT-half of the Argand Plane => must Add 180 degrees Complex Number Calcs cont Consider Two Complex Numbers The PRODUCT n•m The SUM, Σ, and DIFFERENCE, , for these/

##### Complex Numbers One Mark Questions PREPARED BY:

+ b22)(a32 + b32) (d) (a12 + a22 + a32)(b12 + b22 + b32) Choose the Correct Answer 7. The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram in order if and only if (a) z1+ z4 = z2 + z3 (b) z1+ z3 = z2 + z4 (c) z1+ z2 = /z3 + z3 (d) z1 – z2 = z3 – z4 8. If a = 3 + i and z = 2 – i, then the points on the Argand diagram representing az, 3az and – az are (a) vertices of a right angled triangle (b) vertices of an equilateral triangle (c) vertices of an isosceles triangle (d) /

##### Few-body systems as neutron targets A. Fix (Tomsk polytechnic university) 1.

spectator model:  Orthogonality relation: γd→π 0 np Amplitude:  dσ/dΩ suppressed at θ π → 0  Orthogonality is ignored is a plane wave andare eigenstates of the same Hamiltonian 15 200 Absorption of pions 400600800 Photon energy [MeV] 0 2 4 6 x10 2 σ [μb] σ/the resonance region ΔQ ~ 2/Γ R strong influence of inelastic channels Example: ηd elastic scattering in the S 11 (1535) region Argand diagram for L=0Inelasticity parameter Three-body calculation S 11 (1535) Complex nuclei: σ(γA → ηX) ~ A 2/3 (surface /

##### One Mark Questions. Choose the Correct Answer 1.If p is true and q is false then which of the following is not true? (a) ~ p is true (b) p  q is true.

) | z | 2 (c) 2| z |(d) 2| z | 2 29.If a = 3 + i and z = 2 – 3i then the points on the Argand diagram representing az, 3az and – az are (a) vertices of a right triangle (b) vertices of an equilateral triangle (c) vertices of an isosceles triangle (d) collinear Choose / and is (a) (2, 1, 1) (b) (1, 2, 1) (c) (1, 1, 2) (d) (1, 1, 1) 34.The distance from the origin to the plane is (a) (b) (c) (d) Choose the Correct Answer 35.If,, are three mutually perpendicular unit vectors, then | + + | = (a) 3 (b) 9 (c) 3  /

##### Electrical and Computer Systems Engineering Postgraduate Student Research Forum 2001 WAVELET ANALYSIS FOR CONDITION MONITORING OF CIRCUIT BREAKERS Author:

map shows a series of condition vectors derived from 20 tests. This map is a visual representation of the condition of the circuit breaker represented as a point in an Argand plane. METHODOLOGY The Wavelet Packet Transform is originally applied to the fault diagnosis of circuit breakers and the algorithm is tested using the real data collected. The wavelet maxima are used/

##### Honors Pre-Calculus 11-4 Roots of Complex Numbers Objective: Find roots of complex numbers Graph complex equations.

of these numbers you get 1. (Try it and see!) We found the cube roots of 1 were: Lets plot these on the complex plane about 0.9 Notice each of the complex roots has the same magnitude. Also the three points are evenly spaced on a circle. This will /always be true of complex roots. each line is 1/2 unit This representation known as Argand diagram Steps to Find Roots of Complex Numbers 1)Change complex number to polar form z = r cis θ 2)Find the nth roots: 3/

##### ENGR-25_Functions-1.ppt 1 Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Bruce Mayer, PE Registered Electrical.

Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods Complex No.s – Graphically x y r  z = x + i y Im(z) Re(z) The Argand diagram Modulus (magnitude) of z arctan  = arg z = x y + , if x < 0 arctan xy, if x > 0 r = mod z =//Physics 25: Computational Methods Complex Number Calcs  Consider a General Complex Number  This Can Be thought of as a VECTOR in the Complex Plane  This Vector Can be Expressed in Polar (exponential) Form Thru the Euler Identity  Where  Then from the Vector Plot x y r/

##### Particle Physics II Chris Parkes CP Violation Parity & Charge conjugation Helicity of the neutrino Particle anti-particle oscillations CP violation measurement.

Unitarity Triangle Three complex numbers, which sum to zero Divide by so that the middle element is 1 (and real) Plot as vectors on an Argand diagram If all numbers real – triangle has no area – No CP violation Real Imaginary Hence, get a triangle ‘Unitarity’ or ‘CKM triangle’ /Triangle if SM is correct. Otherwise triangle will not close, Angles won’t add to 180 o 23 Unitarity conditions hence 6 triangles in complex plane j=1,3 No phase info. j,k =1,3 j  k db: sb: ds: ut: ct: uc: 24 CKM Triangle -/

##### Superposition of Waves s. Superposition of water waves.

many waves Complex method of Addition Resultant of N waves Complex amplitude of the resultant wave For N=2 Phasor Addition of Waves Argand Diagram Representation of a complex number in terms of real and imaginary components In Complex plane A Sin  t A Cos wt Re Rotating Arrow + Associated Phase Angle = Phasor Addition of two phasor Resultant Addition of three phasor/

##### 11 EM Waves Characteristics and Properties. 2 Electromagnetic spectrum.

time set the derivative to zero 35 Principle of superposition 35 36 Principle of superposition 37 38 Resultant phasor Phasor Addition of waves Argand Diagram Representation of a complex number in terms of real and imaginary components In Complex plane A Sin  t A Cos wt Re Rotating Arrow + Associated Phase Angle = Phasor Addition of two phasor Resultant Addition of three phasor/

##### 1 The Discrete Fourier Transform Leigh J. Halliwell, FCAS, MAAA Brian Fannin, ACAS, MAAA

CAS antitrust compliance policy. 3 Outline I.Complex Numbers II.Roots-of-Unity Random Variables III.Collective-Risk Model IV. Examples 4 I. Complex Numbers Basic Arithmetic Complex Plane versus Real Line Wessel(1979)-Argand(1806) diagram [Kramer, 73] No trichotomy between complex numbers 5 I. Complex Numbers (Cont’d) Completeness of Complex Numbers Fundamental Theorem of Algebra [Kramer, 71] Actuaries should/

is the modulus of z, orIf is the modulus and is always positive or If what is is the complex conjugate of z. Graphing Complex Numbers use the Argand Diagram or the Complex Plane. x-axis would be the real numbers y-axis would be the imaginary numbers Graph the complex number z = 2 + 3i Graph the complex number z = -4i If/

##### Corsi di laurea magistrale in Ingegneria dei Sistemi Idraulici e di Trasporto - Gestionale Corso di GESTIONE DEI SISTEMI DI TRASPORTO “Informazioni all’

can be analyzed with reference to a transformed problem in which:  Associated eigenvalues depends only on J c (f) and J f (c)  The eingenvalues have to be (in the Argand-plane of the imaginary numbers) within an elipse that only depends ○ On α and β in absence of ATIS ○ On α, β and max in presence of (accurate) ATIS  The effect of max is to/

##### IoP Masterclass B PHYSICS Tim Gershon University of Warwick March 18 th 2009.

Gershon, IoP Masterclass, March 18 th 2009 The Unitarity Triangle ● Squares of CKM matrix elements describe probabilities ⇒ matrix must be unitary 12 Three complex numbers add to zero ⇒ triangle in Argand plane Tim Gershon, IoP Masterclass, March 18 th 2009 The BABAR Experiment 13 ● PEP-II accelerator collides electrons and positrons at energies tuned to produce pairs of B mesons ● Electron/positron/