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Complex Analysis

Complex Variables 115: Bonus Question.

All steps must be shown, even small details. Workout the relevant calculations please complete the problem, not just set it up. Provide common sense explanations. Bonus: The function p(z)=[z(z+1)]^-1 can be written in two different ways: (see attached for full equation) These two expansions are contradictory. The first

Complex Variables Calculations.

All steps must be shown, even small details. Workout the relevant calculations please complete the problem, not just set it up. Provide common sense explanations. 6. For a>0, use residue calculus to evaluate (see the attachment for the full problem description and equation.)

Hint: First consider what curve z...

Compute: lim as r -> infinity |f(z)|, where z = re^[(i)("alpha")] Your answer will depend on "alpha". Hint: First consider what curve z = re^[(i)("alpha")] traces out in the complex plane as r -> infinity

Complex Variables. 1.2

What are all possible solutions of z^4 + 4 = 0? From this information, write out a complete factorization of z^4 + 4.

Solve a complex variable equation.

Z is a complex number, s and t are real numbers. Find z1 and z2 - the solution the solutions of the equation. (z^2)+(|z|^2)-(2Is)=(8t^2) in terms of s and t. If z1*z2=-8I find s,t

Calc II

Find the open interval of convergence and test the endpoints for absolute and conditional convergence.

Matlab help for solving non-linear equations

[note: suggested number of credits may be modified if necessary] Hi, Part (1/2) I need help/advice in solving non-linear equations using Matlab. My focus is on the - Bisection method - Regula falsi - Muller's method (if possible) I have seen programs for the above methods on the internet, but I could not see *e

Riemann Sum

Write out the Riemann Sum R(f,P, 1, 4), where f(x) = ln x, P = {1, 2, 2.4, 2.9, 3.4, 4} and ck is the midpoint of the interval [xk−1, xk] for each k. Get a decimal approximation for the Riemann Sum.

Help with an intro analysis proof

Due to the amount of symbols in the problem I attached a .pdf file. In words, I think the problem is asking - if the limit of f at c is positive, then on some deleted neighborhood of c, f is positive away from 0.

Poincare's Lemma and its Converse

Please see the attached file for the fully formatted problem. For  phi E C2[R3 ! R3], curl grad phi = 0. Prove this. The converse is "Poincare's Lemma": if f E C1[R3 --> R3] and if curl f = 0, then f is a gradient, i.e., f = grad  for some  2 C2. Try it this way: if f = grad phi, then phi (x1, x2, x3) = phi(0)+ ....

College Algebra

Can you please help me with these. I can not get these and I am trying to study for the clep exam. Do not do the circled problems only the ones listed below. Thank you for help. Please show step so that I can understand better. 129 1. a) 6, b) 12, c) 16, d) 20 2. a) 24, b) 26 3. a) 35, b) 36 4. a) 46, b) 48 P. 14

Pre calc

Need equation for: Ellipse Center at(0,4); focus at(8,4); vertex at (6,7)

Sequential Compactness

Please see the attached file for the fully formatted problems. Consider C[0, 1], the space of real valued continuous functions defined on the unit interval [0, 1]. Let K = C1[0, 1] {f : Z 1 0 f02  1, ||f||1  1} Note that C1[0, 1]  C[0, 1], and K  C[0, 1]. Show that K is compact in C. I am assuming compactness h

Algebraic series of complex numbers

Given an algebraic series with the following properties: The first term: a1=k-7i The difference: d=-1+2i The sum of the first n terms: S=-5+20i Find k

Cardinality for Irrational Numbers

1. Find the cardinality of the set of all irrational numbers, and prove your answer is correct. 2a. Is there a line in the x-y plane such that both coordinates of every point on the line are rational? Prove your answer is correct. 2b. Find the cardinality of the set of all complex numbers, and justify your answer. 3a. W

Electromotive Force : Minimizing Time

For an electric circuit, let V=cos 2pi(t) model the electromotive force in volts at t seconds. find smallest positive value of t where 0<and= to t<and= to 1/2 for the values a) V=0 b) V=.5 c) V=.25

Polynomial Proof

Suppose P is a polynomial with real coefficients and P(a+bi)=0. Prove (a-bi)=0

Complex Plane that are the Vertices of a Parallelogram

Find necessary and sufficient conditions (with proofs) such that the points z1, z2, z3, and z4 in the complex plane are the vertices of a parallelogram. I have read that the points z1, z2, z3, and z4 in the complex plane are vertices of a parallelogram if and only if z1 + z3 = z2 + z4. But, if this is indeed the case I would li

Understanding how to use the Queing Theory - Erlang M/G/s/GD/s/infinity.

How do I solve a formula or equation for the Erlang System M/G/s/GD/s/infinity that predicts resource requirements (how many servers) using the known variables (1) new events per unit of time; (2) average time per event; (3) event time service level (must be resolved by duration); (4) percent of events that must meet that event