Complex Definition and 1000 Threads

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...

I need recommendation about complex analysis book. As I'm electrical eng. student, it should cover everything one engineer need to know about that mathematical field, but without strict mathematical formalism :)

When I solve a quadratic equation I need to find a Discriminant. If D>0 I have no problem. I can find x1 and x2. And when I draw a parabola I can see the x1 and x2 on a X-line. But when D<0 I don't understand where I can find x1 and x2 on a plot of function. For example for 5x2+2x+1=0 I...

Calculate ( minus ( 2 over 3 ) + ( 2 over 3 ) i ) to the power minus 4, simplifing your answer and giving it in the form a + i b, with a and b given exactly.I found the modulus by: sqrt((-2/3)^2 + (2/3)^2) = (2*sqrt(2))/3 the argument is: pi - 1 (from a sketch in the complex plane) hence...

Hello, I'm trying to derive the perfectly matched layer for the TM mode Maxwell's equations using a complex coordinate stretching. As seen in http://math.mit.edu/~stevenj/18.369/pml.pdf . But I'm running in a bit of trouble somehow. \partial_t H_x =-\mu^{-1} \partial_y E_z\\ \partial_t H_y...

Homework Statement Show that if P(z)=a_0+a_1z+\cdots+a_nz^n is a polynomial of degree n where n\geq1 then there exists some positive number R such that |P(z)|>\frac{|a_n||z|^n}{2} for each value of z such that |z|>R Homework Equations Not sure. The Attempt at a Solution I've tried dividing...

Why do Complex Numbers arise in Quantum Mechanics' computations? What kind of physical significance do they carry? Someone told me to read this paper: W E Baylis, J Hushilt, and Jiansu Wei, Why i?, American Journal of Physics 60 (1992), no. 9, 788–797. But I found it difficult for me to...

If QM is a statistical model to approximate something underlying space time we don't quite understand yet, and there is a complex geometry underlying space time, is it possible to find other ways to simplify molecular optimizations and electron interactions in computational chemistry using...

Here's a link to a professor's notes on a contour integration example. https://math.nyu.edu/faculty/childres/lec12.pdf I don't understand where the ##e^{i\pi /2} I## comes from in the first problem. It seems like it should be ##e^{i\pi}## instead since ##-C_3## and ##C_1## are both on the real...

The way I understand it, they both have rectangular forms which are easy for addition/subtraction. Now I realize that the polar form of a complex vector can be simplified into an exponential, which is ideal for multiplication/division. But this is what confuses me; vectors don't multiply/divide...

I'm going to ask a very general question where I just would want to hear different possible methods that can be thought of in this kind of problem. I am trying to solve a very specific problem with this but I won't talk about that because I don't want someone to give me the answer but ideas for...

Homework Statement The largest value of r for which the region represented by the set { ω ε C / |ω - 4 - i| ≤ r} is contained in the region represented by the set { z ε C / |z - 1| ≤ |z + i|}, is equal to : √17 2√2 3/2 √2 5/2 √2 Homework Equations complex number = a + ib where a,b ε R The...

Hi, so I need to write a fortran code with 2, 2x2 matrices. These matrices are in the form of B=(1 exp(i)(theta) 0 0) and D=(0 0 exp(i)(theta) 1) where i is sqrt of -1 and theta is an angle between 0 and 2pi. I've expanded the exponential so it reads cos(theta)+isin(theta) and let theta=pi/2...

Homework Statement Homework Equations phasor forms voltage division current division The Attempt at a Solution Using superposition, considering only the varying voltage source. Z (L) = 4j Z (C) = 5j Total impedance: 4 is parallel with 5 = 2.44 + 1.95j series with 1 + 4j Total...

Hello, I am trying to understand how to get the residue as given by wolfram : http://www.wolframalpha.com/input/?i=residue+of+e^{Sqrt[x^2+%2B+1]}%2F%28x^2+%2B+1%29^2 The issue I am facing is - since it is a second order pole, when I try to different e^{\sqrt{x^+1}} I get a \sqrt{x^+1}...

Homework Statement In each case, state whether the assertion is true or false, and justify your answer with a proof or counterexample. (a) Let ##f## be holomorphic on an open connected set ##O\subseteq \mathcal{C}##. Let ##a\in O##. Let ##\{z_k\}## and ##\{\zeta_k\}## be two sequences...

Homework Statement Good day, I've been have having difficulties finding the roots of this: Find the roots of 3ix^2 + 6x - i = 0 where i = complex number i = sqrt(-1) Homework Equations quadratic formula (apologies for the large image) The Attempt at a Solution...

Looking for the general equation for repeated complex conjugate roots in a 4th order Cauchy Euler equation. This is incorrect, but I think it is close: X^alpha [C1 cos(beta lnx) + C2 sin(beta lnx)^2] I think that last term is a little off. Maybe C2 sin [beta (lnx)] lnx ?

Edit: Sorry about the vague title, it was intended to be complex beam system boundary conditions but somehow it turned out like this. Hello, I am trying to learn complex beam system designs and I sometimes struggle to assign boundary conditions. For example I am trying to design the lifting...

(@mfb posted an article about this here, I think it deserves an own thread, and I did not find one, so I start one :smile:) The comet-like composition of a protoplanetary disk as revealed by complex cyanides Karin I. Öberg, Viviana V. Guzmán, Kenji Furuya, Chunhua Qi, Yuri Aikawa, Sean M...

Homework Statement How would Re(z)<0 be graphed? Homework Equations Re(z) is the real part of z The Attempt at a Solution It looks similar to y>x, but only shaded in the third quadrant, how can this be explained? not relevant anymore