Share
Explore BrainMass

Complex Analysis

Multiplication of Complex Numbers

Is the multiplication of complex numbers similar to multiplication of polynomials? Is it possible to apply the FOIL method when multiplying complex numbers? Explain your answers.

Process Capability Analysis

You are the process improvement manager and have developed a new machine to cut insoles for the company's top-of-the-line running shoes. You are excited because the company's goal is no more than 3.4 defects per million (very close to zero defects) and this machine may be the innovation you need. The insoles cannot be more than

complex numbers - moduli

I have two problems with complex numbers: 1) Use properties of moduli to sow that when |z3| does not equal |z4|, Re(z1 + z2) / |z3 + z4| <= (is smaller or equals) (|z1| + |z2|) / (| |z3| -|z4| |) 2) Verify that sqrt(2) * |z| >= |Re z| + |Im z| (suggestion: reduce this inequality to (|x| - |y|)^2 +. 0

expand on equations 1 and 2

see attached please expand on and explain the attached work ie how does one make the transformations shown in equation 1 and 2 and 3...please show this work in complete, painful detail I have given this as a new post as I believe it is outside the original post

Question about Complex numbers in Polar Form

Plot the complex number. Then write the complex number in polar form. Express the argument as an angle between 0 and 360degrees. 2 Z = ? (cos ? + i sin ? ) (type an exact answer in the first answers, type all degree measures rounded to one decimal place)

DeMoivre's Theorem for finding Complex Roots

Find all complex fourth-roots in rectangular form of w= 121 ( cos 2pi/3 + i sin 2pi/3 ) Type answer in the form a + bi round to the nearest tenth. Zsub 0 = ? + ?i Zsub 1 = -? + ?i Zsub 2 = -? - ?i Zsub 3 = ? - ?i

Demoivre's Theorem for Finding Complex Roots Degrees

Find all the complex cube roots of w= 8(cos 150 + i sin 150). Write the roots in polar form with theta in degrees. answers look like; z sub 0 = ? (cos ?degrees + i sin ?degrees) z sub 1 = ? ( cos ?degrees + i sin ?degrees) z sub 2 + ? ( cos ?degrees + i sin ?degrees) First build the expression for x sub k with r=8, th

Complex Numbers in Polar Form; DeMoivre's Theorem

Write the expression in the standard form a + b i (sqrt 2 + i)^4 Write the result in a + b i form First convert to rectangular form--- calculate the magnitude-- find reference angle--then the argument of z--- Type answer in the form a +bi. Do not round until the final answer. Then round to the nearest thousandth as nee

Taking the complex conjugate

Hello. I am trying to derive the attached expression from my textbook, but I am not able to understand, it involves taking the complex conjugate, where the overbar indicates complex conjugate. ** Please see the attached file for the complete problem description ** Thanks!

Statistics

Measurement Error And Data Representation 1. State whether or not this statement is true or false, and explain: " An experienced scientist who is using the best equipment available only needs to measure things once—provided he doesn't make a mistake. After all, if he measures the same thing twice, he will get the same resul

Solving Complex Perimeter & Area problems

1.How could you define the perimeter of a nonsimple closed curve? What would an example be? You don't need to draw anything just describe. 2.Find the area of the shaded parts. Assume all arcs are circular. Leave all answers in terms of pie.

Breakeven Analysis for Micromedia

Micromedia offers computer training seminars on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting. Micromedia is currently planning a two day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for t

Find the value of the discriminant.

State the value of the discriminant and then describe the nature of the solution. -15x^2+7x+2=0 What is the value of the discriminant? _______ Does the equation have..... Two imaginary solutions Two real solutions OR One real solution

A Taylor Series Problem

i) Use the Taylor Series for 1/(1-x) to find the Taylor Series of 1/(1+x) about x = 0 and its Interval of Convergence. ii) Use the result of part (i) to find the Taylor Series of ln(1+x) about x = 0 and its Interval of Convergence. iii) Use the Taylor Series found in part (ii) to approximated ln(1.1) up to five decimal pla

Residues, essential singularities and integrals

1. Find where is the function f(z) = 1/((2z-1)(Log(2z)) analytic, and then find all residues in all isolated singular points. 2. Evaluate: Integral((exp(1/z)/(z-1)dz)), where the curve is IzI =2, oriented positively.

A convergent sequence

Let (X,d) be a metric space with x in X and A as a nonempty subset of X. The distance between x and A is defined as: dist(x,A) = inf{d(x, a) : a in A} i > 0 A_i = {x in X : dist(x,A) <= i} a) Show that A_i is closed b) C is a collection of all compact subsets of X. C is nonempty p : C Ã? C -> [0,infinity

Bore-Cantelli Lemma

Let {f_n} be a sequence of measurable functions on [0,1] with |f_n (x)| < infinity for a.e x. Show that there exists a sequence c_n of positive real numbers such that f_n (x) / c_n -------> 0 a.e.x. Hint: Pick c_n such that m ({x : |f_n (x) / c_n| > 1/n} ) < 2^(-n), and apply the Bore-Cantelli Lemma.

Proof of Measurables

If delta = (delta_1, ..., delta_d) is a d-tuple of positive numbers delta_i > 0, and E is a subset of R^d, we define delta E by delta E = {(delta_1 x_1, ..., delta_d x_d) : where (x_1, ..., x_d) belongs to E}. Prove that delta E is measurable whenever E is measurable, and m(delta E) = delta_1 ... delta_d m(E).

Laplacian, real/imaginary parts, derivatives of complex numbers

Studying for a midterm and could not get the following practice problems. 1. Find the Laplacian (d^2f/dx^2 + d^2f/d^y^2) for a. f(x,y)=x^2-y^2 b. f(x,y)= (x^2-y^2) / (x^2+y^2) ((x,y) not equal to (0,0)) c. f(x,y)=(x^2-y^2) / (x^2+y^2)^2 ((x,y) not equal to (0,0)) 2. Calculate the real part and the imaginary part

DeMoivre's theorem

Suppose we want to find the nth root of a complex number z; that is, we want to find w such that We write z and w in the form Using DeMoivre's theorem we have (using the equation ) i) Show that the absolute value of wn and z are equal. Hence find R in terms of r. ii) Equate the arguments of wn and z to find a

Riemann sum and Continuity

Given f(x)=x^3 on [0,1] and the partition P={0,1/8,1/3,2/3,1}, find four different Riemann sums R(f,P). Show that Chi_Q is discontinuous at every point where Chi_Q is the characteristic function for Q - Rational numbers.

Quantitative Analysis: Networks, PERT and Critical Path

In one of the little-know battles of the Civil War, General Tecumseh Beuregard lost the Third Battle of Bull Run because his preparations were not complete when the enemy attacked. If the critical path method had been available, the general could have planned better. Suppose that the following planning network, with activity t

Gaussian elimination diagram

1. Solve the following system of equations by hand. Use the Gaussian elimination, on the augmented matrix, and write the row operation you used next to each new row. x + y + z = 0 3x - 2y + 2z = -14 2x + 3y - z = 22 2. Find all roots of the equation z^5 = i, i.e. find the five values of i^(1/5) and show them on an Argand

Solve the equation sinz=2 for z by

Solve the equation sinz=2 for z by: a) equating real parts and then imaginary parts in that equation b) using sin^-1(z)=-ilog[iz+(1-z^2)^1/2]

Pully equation with complex numbers (Cartesian/Polar)

Task 3 For the pulley shown below, the tension T in the cable is 100N. First express each tension in Cartesian form and add these together to find the resultand force on the pulley shaft of diameter 12mm. Then express the resultant force in Polar form. Hence determine the shear stress in the pulley shaft. given that it is in do

Derive the complex form of the Cauchy-Riemann equations.

Recall that if z=x+iy then, x=(z + zbar)/2 and y=(z-zbar)/2. a) By formally applying the chain rule in calculus to a function F(x,y) of two real variables, derive the expression dF/dz=(dF/dx)(dx/dz)+(dF/dy)(dy/dz)=1/2((dF/dx)+i(dF/dy)). b) Define the operator d/dz=1/2((d/dz)+i(d/dy)) suggested by part (a) to show that i

set of complex numbers

1.Find an example of a sequence an of complex numbers such that the series SUM a_n converges (conditionally), yet the series SUM a^(3)_n diverges. 2.Determine the set of complex numbers z for which the series SUM(1â?'z^2)^n converges. SUM means sigma.

Waiting line analysis

Student arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eights hours per day. Assume Poisson arrivals and exponential service times. A. What percentage o