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Complex Analysis


I need to find all real or imaginary solutions to this equation. Please see attached

Evaluating complex numbers

Given the complex numbers z1 = 5 - j4 z2 = 4 + j z3 = -6 - j7 z4 = j2 Calculate, giving your answers in the form a + jb, the following:- (i) z4 - z1 + z2 (ii) 3z1 - 2z3 + z4 (iii) z1z2 (iv) z3/z2

Solve complex equation

In the following equation by equating real and imaginary parts, find expressions for R6 and L in terms of R1, R2, R3, R4, R5 and C, given that the frequency is one radian per second. See attached file for full problem description.

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

Systems of Complex Equations

x ------------------ = 0.007 754 1 + i --------- y 42425 x -------------------------------------- = 1 754 (1+ i -------) *500* (1 + i 41.47) y USING THESE TWO EQUATIONS SOLVE FOR X=? AND Y=?

Mobius Transformations

Prove that if T is a Mobius transformation such that T(0) = 0, then T may be written as T(z) = z/(cz+d) for some choices of c and d.

Complex Number Form : a+bi

Write each expression in the form of a+bi, where a and b are are real numbers 1. -3i/3-6i 2. -2-sqrt-27/-6

Solve y < -2 + 7

Y < -2 + 7 i need help to solve this equation and the steps on how to solve it.

Complex Variables : Analytic Functions and Limits

Let f(z) be analytic in a region G and set &#966;(z,w) = (f(w)-f(z))/(w-z) for w,z &#1028; G w &#8800; z. Let z0 &#1028; G. Show that lim (z,w)-->(z0,z0) &#966;(z,w) =f'(z0). Complex Variables. See attached file for full problem description

Complex Variables : Analytic Functions and Laurent Series

Any insight on where to go with these problems would be helpful and appreciative. This is my first time in complex analysis and I am having problems understanding the concepts. Seeing solutions to problems is helping me to understand how to approach other problems. Thank you very much! I need help specifically on problems

Complex Variables : Rectafiable Path

Fix w=re^i&#952;&#8800;0 and let gamma be a rectafiable path C-{0} from 1 to w. Show there is an integer k such that &#8747;gamma z^-1 dz = log r + i&#952; + 2 pi i k See attached file for full problem description.

Solving Complex Equations

I need to solve for all of the roots of (z+1)^4 = (1-i). Any idea on how to do it? keywords: imaginary

Verifying a Complex Root

Verify the z = (3-2j) is a root of the polynomial 2z^4 - 18z^3 +66z^2 - 102z + 52 and hence find the other three roots.

Real Analysis : Complex Power Series and Radius of Convergence

2. First do Problem #24 on p. 163 (as usual, using Problem 5 below to justify replacing roots by ratios in the definition of the radius of convergence). Then note that since the power series in question has radius of convergence 1, we can replace the real variable x with a complex variable z and then use the power series as the

Solutions to equation

Let lambda be real and lambda > 1, Show that the equation ze^lambda&#8722;z = 1 has exactly one solution in the disc |z| = 1, which is real and positive.

Complex Numbers, Standard Form and DeMoivre's Theorem

1. Evaluate the expression and write your answer in the form a+bi: i^100 2. Prove the following properties of complex numbers. 3. Find all solutions of equation:- 4. Find the indicated power using De Moivre's Theorem. .