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# Complex Analysis

### Data Analysis: Standard Deviation

I think that I did the first part right I just need reassurance, but I am really having difficulty with finding the percentage. Do you think that you could help? Using the sample data here 55, 52, 76, 40, 50, 65, 40. State the mode, Find the median, and state the mean. The sample standard deviation is 13.0. What percent

### Statistical Analysis in a Random Sample

You select a random sample of n=14 families in your neighborhood and find the following family size (number of people in the family). 6 7 10 9 8 6 7 7 6 7 6 7 8 9 a) What is the mean family size for the sample? I think the answer here is all the above #'s * 14=7.37143 The mean family size for the sample is _7.36

### Minimum Sample Size Analysis

One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.25 hour is desired. Past studies suggest that a population standard deviation of 1.7 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the s

### Complex Variables and Applications

f(z) is defined by the equations: f(z)=1 when y<0 and f(z)=4y when y>0, and C is the arc from z=-1-i to z=1+i along the curve y = x^3. The answer is given as 2+3i. For C1 I get z=-x-ix^3, but the book says it is x+ix^3 (-1<x<0).

### Simplify the expressions involving complex numbers.

Express each number in terms of i and simplify. p + sqrt(-81) Add -- (2 + 6i) + (7 - 4i) Subtract as indicated -- (4 + 3i) - (10 - 4i) Find the product -- 8i (3i - 2) Find the product -- (7 - 6i)(8 - 3i)

### 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.

### Complex number based inverse trigonometric function

Find all values of: tan^(-1) * (1 + i) The format for the final answer should be similar to this one: if the problem is tan^(-1) * (2i). answer: (n + 1/2)*pi + (i/2) * ln(3) , (n =0, +-1, +-2,...)

### Polynomial Question: Galois group is S7

Find a polynomial of degree 7 over Q whose Galois group is S7.

### 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

### The Domain of a Complex Function

For each of the functions below, describe the domain of definition that is understood: a) f(z)=1/(z^2+1) b) f(z)=Arg(1/z) c) f(z)=z/(z+z bar) d) f(z)=1/(1-|z|^2 )

### 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

### Introduction to Complex Conjugates and Imaginary Numbers

What are complex numbers? What does imaginary parts of equal magnitude and opposite signs mean? What is the quadratic formula? What is it used for? Provide a useful example.

### 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 onceâ€”provided he doesn't make a mistake. After all, if he measures the same thing twice, he will get the same resul

### Rotations and complex numbers.

Solve 1-4 in the attachment.

### 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.

### Singular points and residues of 1/[(Cosh(z))-2exp(z)]

Classify all singular points of f(z) = 1/[(Cosh(z))-2exp(z)] and find all residues.

### 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 Ãƒ? 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