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Complex Analysis

Determine if the following equations are real or complex.

Determine if the following equations are real or complex; explain the answer in detail. Determine whether the following equations real or complex solutions; justify your answer. Note: It is not necessary to find the solutions; just determine if they are real or complex and explain why. a) 5x2 + 8x + 7 = 0 b) (7)1/2y2 - 6

Are the roots real, repeated real, or complex?

Determine if the following have a solution or not? justify answer. (apply the discriminant) are the roots real, repeated real, or complex? 1) 5x^2+8x+7=0 2) (7)^1/2y^2-6y-13(7)^1/2=0 3) 2x^2=x-1=0 4) 4/3x^2-2x+3/4=0 5) 2x^2+5x+5=0 6) p^2-4p+4=0 7) m^2=m+1=0 8) 3z^2+z-1=0

Solve the triangle and complex number

Please see attached file for full problem description. 1. B = 54 degrees, C = 112, and b = 18 2. Solve the equation on the interval [0, 2pi]: (cosx)^2 + 2 cos x + 1 = 0 3. Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. C = 110°, a = 5, b = 11 4. Solve the triangle.

Quantitative Analysis - Waiting lines and queuing Theory models

I have some Quantitative Analysis questions I need help understanding. Waiting lines and queuing Theory models 1. The New Providence shopping mall is considering setting up an information desk manned by one employee. Because of the complex design of the mall, it is expected that people will arrive at the desk at about twi

Complex Variables, Laurent Series and Uniform Convergence

(1) Let G = {z : 0 < abs(z) < R} for some R > 0 and let f be analytic on the punctured disk G with Laurent Series f(z) = sum a_n*z^n (from n = -oo to oo). (a) If f_n(z) = sum a_k*z^k (from k =-oo to n), then prove that f_n converges pointwise f in C(G,C) (all continuous functions from G to C (complex)); i.e., {f_n}

Derivation of Poisson Integral Formula for the Half-Plane

If is analytic in a domain containing the x-axis and the upper half-plane and in this domain, then the values of the harmonic function in the upper half-plane are given in terms of its values on the x-axis by (y>0). Below is an outline for the derivation, I just need to figure out how to justify the steps.

Quantitative Analysis in Business Decisions

Mr. Davison has been operating a small bicycle shop at the same location near Aspen, Colorado for 50 years. What type of decisions must he make in operating his business? On what basis would he likely be making these decisions? How do you think Mr. Davison would respond to a suggestion that he hire a quantitative analyst to assi

Complex Variables : Analytic Functions and Limits

Please help with the following mathematics-related problem. Let f(z) be analytic in a region G and setphi(z,w) = (f(w)-f(z))/(w-z) for w,z E G w does not equal z. Let z0 Ye G. Show that lim (z,w)-->(z0,z0) phi(z,w) =f'(z0). Complex Variables. See attached file for full problem description

Complex Variables: Rectifiable Path

Please help with the following problem. Fix w=re^i(theta)(not equal)0 and let gamma be a rectafiable path C-{0} from 1 to w. Show there is an integer k such that (integral)gamma z^-1 dz = log r + (theta)+ 2 pi i k See attached file for full problem description.

Stereographic Projection

1. Let z and z' be points in C with corresponding points on the unit sphere Z and Z' by stereographic projection. Let N be the north pole N(0,0,1). a) Show that z and z' are diametrically opposite on the unit sphere iff z(z bar)'=-1 ps. here z bar means conjugate of z b) Show that the triangles Nz'z and NZZ' are similar. The

Projective geometry hyperplane

Projective Geometry Problem 4 Let C be the curve in a complex affine plane E. Find the infinite points of C, i.e. the points of the projective closure of that lie on the hyperplane at infinity. See attached file for full problem description.

Catenary Model

A) Graph the model b) Find the heights of the cable at the towers and at the midpoint between the towers, and c) Find the slope of the model at the point where the cable meets the right-hand tower y = 18 + 25cosh x/25, -25 &#8804; x &#8804; 25

Riemann Sums

Please see the attached file for the fully formatted problems.

Logarithms and Complex Numbers

1. Given that s = 1.59t(1-3v), obtain the value of v when s = 3.52 and t = 21.56. 2. Solve log(2x + 3) = log(4x) + 2, for x giving the answer correct to 3 significant figures. 3. For a thermodynamic process involving a perfect gas, the initial and final temperatures are related by: T1 exp(^s/Cp) =

Finding a Vertex and Vertex Form and Dividing Complex Numbers

1.Find the vertex form of the quadratic function g(T)=2T^2-4T+5 and determine the coordinates of this functions vertex vertex form_______________ the vertex______________ 2. solve problem following equations algebraically showing all work and steps and solutions -2X^4+6X^2-4=0 X=__________________ 3.showing all

Argand Diagram and Complex Impedance

Please see the attached file for full problem description. Show the following complex numbers on an Argand diagram: Given that the equivalent impedance of parallel complex impedances in an electric circuit is given by: calculate the equivalent impedance br the following circuit.

Question: complex number in polar form

(See attached file for full problem description) 1. simplify each of the following: giving your answer as a complex number in polar form: 2. Convert the following complex numbers in polar form to rectangular (a+jb) from:

Algebra: Complex Roots and Solutions, De Moivre's Theorem and Argand Diagrams

1 Find the real and complex solutions of these cubic equations. a) (z-3)(z2-5z+8)=0 b) z3 - 10z2- 34z- 40 = 0, given that 3-i is a root (solution). 2 Solve the equation z3 = 125 cis 45 3 Consider the complex number: z = = cos + z sin a) Use De Moivre's theorem to find z2, z4 and z6. Leave your answers in polar form. b) Pl