### Complex Analysis - Analytic Functions

Please answer the attached complex analysis questions. i.e. Prove the following generalization of proposition ... if g is analytic, if f is analytic.

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Please answer the attached complex analysis questions. i.e. Prove the following generalization of proposition ... if g is analytic, if f is analytic.

Please answer the attached complex variable problems. Thank you.

Please see the attached file for full problem description. --- Show all steps, even minor details Send response as attachment Provide common sense explanations Determine a branch of log that is analytic at z = -1, and find its derivative there.

Find the limit of f(z) = x^2/(x^2+y^2) +2i Where z=x+iy and |z| --> 0. See the attached file.

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

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.)

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

All steps must be shown. Please provide explanations in complete sentences Simplify each of the following as much as possible (in other words, write each in the form a + bi). (b) (1 + 2i)^3 (c) 1/(1 +2i) (g) Compute (e) where Your answer will depend

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

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

See attachment

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

Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, do so.

Find (1+i)^100

[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

Write out the sum ∑7,k=3 (k2 +/- 3k + 1) and calculate it.

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.

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.

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)+ ....

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

1. Find the number of real roots and imaginary roots: f(x)=10x^5-34x^4-5x^3-8x^2+3x+8 2. Find all zeros: f(x)=x^4+2x^3+5x^2+34x+30 3. Find all roots: f(x)=x^3-7x^2-17x-15; 2 + i 4. Find all roots: f(x)=x^4-6x^3+12x^2+6x-13; 3 + 2i The 5th problem is attached. Please answer the question

I need some help with complex numbers and exponents problems: z^6z^6 = - 64i. Find z all solutions.

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

Step 1: A 240 horsepower car beginning at a stop goes 1/10 of a mile. At optimum performance, what is the maximum speed in miles per hour the car can reach? Feet per minute? Step 2: How many feet have been traveled in a 240 horsepower car when the speed reaches 35 MPH at optimum performance? what fraction of a mile is that dist

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

(5+i).(3-5*i)

A. write 2 + sqrt(-16) in standard form b. (4+i)/(3-2*i)

Sec0 * cos 2*0 = 2*cos0 - sec0

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.

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