Complex Definition and 1000 Threads

Dear All, Please, I am trying to read in a data shown in array form but no luck. The data is 10 by 10 with each 10 by 10 depicted by a local array, for e.g. 0 0 0 0 0 0. A sample of the code I tried using is as shown below and the data is as attached. Please, any help or suggestion will be...

$a>1,b>1$ find the minimum value of $\dfrac {a^2}{b-1}+\dfrac {b^2}{a-1}$

Homework Statement Let 0 < r < 1. Show that from n=1 to n=∞ of Σ(r^ncos(n*theta)) = (rcos(theta)-r^2)/(1-2rcos(theta)+r^2) Hint. This is an example of the statement that sometimes the fastest path to a “real” fact is via complex numbers. Let z = reiθ. Then, since r = |z|, and 0 < r < 1, the...

Hi everyone, I have a dispersive wave packet of the form: ##\frac{1}{\sqrt{D^2 + 2i \frac{ct}{k_0}}} e^{-y^2/(D^2+2i\frac{ct}{k_0})}## The textbook says that the enlargement of the package, on the y direction, is: ##L=\frac{1}{D}\sqrt{D^4+4\left(\frac{ct}{k_0}\right)^2} ## However I have some...

Homework Statement With . Give an example, if it exists, of a non constant holomorphic function that is zero everywhere and has the form 1/n, where n € N. Homework Equations So.. This was in my Complex Analysis exam, and i have no idea what to do. I always seem to get stuck at these more...

1. Given, x + yi = tan^-1 ((exp(a + bi)). Prove that tan(2x) = -cos(b) / sinh(a)Homework Equations I have derived. tan(x + yi) = i*tan(x)*tanh(y) / 1 - i*tan(x)*tanh(y) tan(2x) = 2tanx / 1 - tan^2 (x) Exp(a+bi) = exp(a) *(cos(b) + i*sin(b))[/B]3. My attempt: By...

I have an impedance tube and it gives me the magnitude (dB) and phase (phase) of a signaa. So does that mean the complex pressure at that point is simply the [Magnitude] +i[Phase Value]? Does I need to change the units at all?

Homework Statement This is an easy one, but keep in mind I'm kind of a newbie, anyway I can't figure out how to get the next formula... tan(z) = (tan(a)+i tanh(b))/(1 - i tan(a)tan(b)) Homework Equations This is the third part of an excercise, previous I proof the follow, -all using the...

Show that, for all real p and m, e^{2mi\cot^{-1}(p)}\left(\dfrac{pi+1}{pi-1}\right)^m=1

Hi all, I was unsure where to put this thread as I read the main topic title in the topology/analysis forums and decided to post it here. I am looking for a chart/graph/website that helps me understand the basic terms such as: -neighborhoods -Boundary points -Singularity points - "Function is...

I neet to do a structured triangular mesh 2D of a complex geometry with FORTRAN Can someone help me!

I am currently learning how to work with Cauchy-Riemann equations. The equation is f(z) = 2x+ixy^2. My question: is u(x,y) = 2x or just x? At this link: http://www.math.mun.ca/~mkondra/coan/as3a.pdf in letter e) they say u(x,y) is equal to x. But I don't understand how that is possible. Is...

Dear all, I'd like to know what is the place/use of complex variables (and complex analysis) in classical mechanics. By the way, is there any? Thanks for your help. Best regards!

Homework Statement Find the image of the rectangle with four vertices A=0, B= pi*i, C= -1+pi*i, D = -1 under the function f(z)=e^x 2. The attempt at a solution So, the graph of the original points is obvious. Now I have to map them to the new function. Seems easy enough, but I am not getting...

Hi,I'm facing a problem finding the values of complex numbers, I'll put two examples then I'll explain the issue. ex1: (-e)^{iπ} , my answer is (-e)^{π^2±2mπ^2} The book answer is (-e)^{π^2} ex2: e^{2 arctanh(i)} , my answer is e^{[iπ/2±mπ/2]} = ie^{±mπ/2} The book answer is i...

The problem states, Show that: a) |e^(i*theta)| = 1. Now, the definition of e^(i*theta) makes this |cos(theta)+isin(theta)| If we choose any theta then this should be equal to 1. What can help me prove this? If I choose, say, pi/6 then it simplifies to |(sqrt(3))/2+i/2)| which doesn't seem to...

Use properties to show that: (question is in the attached picture) Now, it is my understanding that due to properties you can express (sqrt(5)-i) as the sqrt((sqrt(5))^2+(-1)^2) which equals sqrt(6). And (2zbar+5) can be represented as (2z+5). But this would be sqrt(6)*(2z+5) which is NOT...

Hi, I'm trying this summer to finish my mathematical methods book. I'm investigating right now the chapter of complex numbers, the end of the chapter has some applications in electricity and how can complex numbers make the work easier. The problem is that I didn't found it easier nor...

Hey, so I just have a quick question. I am trying to set a complex variable (in an array) as ##e^{i\alpha_1}## and the line I used in my code looks like this: hmajphasemix(2,2)=(cos(alpha1),sin(alpha1)) But the compiler is telling me that it "expects a right parenthesis" at this line. I'm...

I'm reading Rudin's principles and so far I really like it. I find charm I'm his terseness, and I think having that motivation to do a lot of the stuff myself makes it pretty fun (like only using the outline of the Dedekind cuts section and prove all the steps myself). However, I have heard not...

I'm working through some examples in a textbook but i am unable to get the desired answer on my calculator, i keep getting math error and various other results which are not the answer I'm looking for. What i have is: √ 62.9∠88.2 / 0.00165∠72.3 Please could someone tell me what answer you get...

Me and a friend at school are doing an honors project for a Computer Science class. We're trying to find the aerodynamic drag coefficient of complicated 3D Shapes entirely virtual. We started out the project with a specific physics engine in mind. It turned out this engine "Bullet Physics"...

Sorry if this is the wrong forum to post this- Can anyone suggest a good (ideally online) resource for challenging complex analysis problems? The ones I have found so far have been mainly computational- I'm looking for conceptually harder problems, preferably requiring lots of proofs, which...

I was wondering about the following Λ=I+iT T are the generators and Λ a continuous LT transformation, thus it is real. Therefore T needs to be imaginary. And we can find two sets one being the generators for SO(3) J_i and the other for boosts K_i, which are both imaginary. Now I am wondering...

How can I solve the integral below? ## \int_{-\infty}^{\infty} \sqrt{k^2+m^2} e^{izk} dk ## I thought about contour integration but, as you can see, it doesn't satisfy Jordan's lemma. Also no substitution comes to my mind!

Find three different complex numbers that satisfy the equation in the form a + bi. I know that: Re(z) = a + bi = a Im(z) = a + bi = b Re(z) = 4Im(z) a = 4b I'm stuck after this point. How do you find what is a and what is b?

I'm trying to understand something in my notes here... So if we call the real part of the complex algebra 'even' and the imaginary part 'odd' then this graded algebra is communitive but NOT graded commutative. so ab = ba for all a and b in C. If we call the whole complex algebra 'even' and...

Hi, I want to transform a complex exponential with quadratic phase to discrete form, in other words to a vector form. can anyone help me with that? Thanks

I have a question about complex reflection and transmission coefficients. For example, I am modeling a wave in air (medium 1) ## \varepsilon = \varepsilon_0 ## reflecting on, and transmitted to, a medium 2 with ## \varepsilon = \varepsilon' -j \varepsilon'' ## If the wave would have traveled...

Hi there, Once again I find myself twiddling around with some quantum mechanics, and I bumped into something I find strange. I can't see what the error of my thinking is, so I hope someone could be able to point it out. I'm looking at solutions to the infinite square well, and arrive at the...

Hey everyone, I'm transferring into UIUC this fall, and I just registered for my classes earlier today. I'm completing dual degrees in physics and math. I've completed the introductory physics sequence, and the introductory calculus sequence, plus a 200 level introductory differential equations...

Here's my situation: Summer 2015, I am majoring in math and physics. I am taking a 4-week course on DIFF EQ right now, and completely loving it and doing extremely well. Just finished my set of Calc 1, 2, and 3, and an intro to advanced math course (proof-writing basics). Diff EQ is a 220...

I am trying to calculate a pole of f(z)=http://www4b.wolframalpha.com/Calculate/MSP/MSP86721gicihdh283d613000033ch4ae4eh37cbd4?MSPStoreType=image/gif&s=35&w=44.&h=40. . The answer in the textbook is: Simple pole at...

The equation for a torus defined implicitly is, $$(\sqrt{x^{2} + y^{2}} -a)^{2} + z^{2} = b^{2}$$ When solving for the z-axis in the torus equation, we get complex solutions, from the empty intersection: $$z = - \sqrt{b^{2} - a^{2}}$$ $$z = \sqrt{b^{2} - a^{2}}$$ I was told by someone that...

i have a a little problem in fortan90 i just wanted to know how to input a complex number ( input real and img part alone ) all i want to do is to make a simple program about DeMoivres Theorem i have been around in google all i know how to declare a argument as complex complex a then how to...

In my math world novel these numbers have come to life and they have 10 operational chromosomes( +, -, *, /, ^, arrow arrow(tetration), nth root, logarithm, super root, and super logarithm). They also have 4 sex chromosomes each of which can be X or Y. With these sex chromosomes it is like this...

Homework Statement Calculate the following limit if it exists ## \lim_{z\to -1}\frac{\sqrt{z}-i+\sqrt{z+1}}{\sqrt{z^2-1}} ## the branch of root is chosen so that ## \sqrt{-1}=i## Homework EquationsThe Attempt at a Solution I tried most of the same things that I tried earlier today (...

Today, I had a class on Complex analysis and my professor wrote this on the board : The Laplacian satisfies this equation : where, So, how did he arrive at that equation?

Suppose we have a complex function f(z) with simple poles on the complex plane, and we know exactly where these poles are located (but we don't know how the function depends on z) Is there any way to build up the exact form of f(z) just from its poles?

Homework Statement Calculate the following limit if it exists: ##\lim_{z\to i} = \frac{z^3+i}{z-i}## Homework Equations Possibly relevant: ## \lim_{z\to\infty} f(z) = \omega_0 \hspace{5mm} \text{if} \hspace{5mm} \lim_{z\to 0} f\left(\frac{1}{z}\right) = \omega_0## The Attempt at a Solution...

Let $[a,b]$ be a closed real interval. Let $f:[a,b] \to \mathbb{C}$ be a continuous complex-valued function. Then $$\bigg|\int_{b}^{a} f(t)dt \ \bigg| \leq \int_{b}^{a} \bigg|f(t)\bigg| dt,$$ where the first integral is a complex integral, and the second integral is a definite real integral...

Biologists split life into two broad categories: prokaryotes and eukaryotes. Prokaryotes are relatively simple single-celled organisms and are split into two groups (bacteria and archaea). Eukaryotes, on the other hand, are much more complex cells containing specialized compartments such as...

Problem: Given $W = \{z: z=x+iy, \ y>0\}$ and $g(z) = e^{2 \pi i z},$ what does the set $g(W)$ look like, and is it simply connected? Attempt: $W$ represents the upper-half complex plane. And $$g(z) = e^{2 \pi i (x+iy)} = \cdots = e^{-2\pi y}(\cos (2 \pi x) + i \sin (2 \pi x)).$$ (Am I on the...

http://www.math.hawaii.edu/~williamdemeo/Analysis-href.pdf Please look at problem 2 on page 39 of the problems/solutions linked above. I know I'm going to kick myself when someone explains this to me but how was equation "(31)" of the solution obtained? The first term of the RHS of (31) is...

Find all complex numbers $x$ for which $(x-x^2)(1-x+x^2)^2=\dfrac{1}{7}$.

I am trying to solve a Duffing's equation ##\ddot{x}(t)+\alpha x(t)+\beta x^3(t)=0## where ##\alpha## is a complex number with ##Re \alpha<0## and ##\beta>0##. The solution can be written as Jacobi elliptic function ##cn(\omega t,k)##. Then both ##\omega## and ##k## are complex. The solution to...

The overall question is on non steady fluid mechanics however the part on stuck on boils down to the two equations below, which I am unable to solve. X = 122.3 (2 - Y) Y= 0.18 * SQRT( 100 + X ) the text states the equations are satisfied by Y = 1.903 and X = 11.82. To prove this isn't a...

Homework Statement Determine whether the sequence zn = n/((1+i)n) converges and rigorously justify your answer. Homework EquationsThe Attempt at a Solution I have attempted an ε-n proof using my limit as 0 (as exponentials grow faster than polynomials I assumed this was the correct limit)...

Homework Statement My homework question says: the uncertainty in length 1 is +/- 0.1 and in length 2 is +/- 0.1 : calculate the percentage uncertainty in V where V L1-L2 is 30Homework Equations V= (1/(L1-L2))^0.5 where L is the length[/B]The Attempt at a Solution So what I did was add...

Homework Statement I am confused about the heating of the unstable complex: ##[Fe(H_2O)_5(NO)]SO_4## In one place I read that it gives ##FeSO_4## , whereas in other place it says ##Fe_2(SO_4)_3##. So which one is correct? Homework EquationsThe Attempt at a Solution I really don't have any clue...