Complex Definition and 1000 Threads

Hi all, I'm preparing for a deferred exam this semester after falling ill last year. Just looking over my course notes and have a question. I understand how this works in the big picture scheme. What I don't understand however is how my instructor simplified the original equation. 1. Homework...

Hello, I am currently trying to parametrize a surface constructed by thickening a rather complicated curve, defining its normal, binormal and tangent vectors. Even using Mathematica simplification, the resulting vectors are page long expressions and the reason for it is because I have four...

Homework Statement I'm going crazy. I've done this problem nearly 20 times and keep getting the same answer. I've read my textbook so many times too! What am I doing wrong? Homework Equations Zcapacitor = 1/(jwC) Zinductor = jwL Zresistor = R The Attempt at a Solution Z for the...

Homework Statement I'm struggling with the proof that the limit of a complex function is unique. I'm struggling to see how |L-f(z*)| + |f(z*) - l'| < ε + ε is obtained. Homework Equations 0 < |z-z0| < δ implies |f(z) - L| < ε, where L is the limit of f(z) as z→z0 .The Attempt at a Solution...

<<Moderator note: Remember that filling in the complete homework template is mandatory in the homework forums. This thread has not been deleted due to containing relevant replies.>> 1. Homework Statement ((x)^(1/x))' Homework Equations This probably isn't overly dificult, but it has got me...

Hi, In my textbook the following theorem is designated "Proposition 3.4.2 part (vi)". There are 6 parts total in the overall theorem. I'll just type the part I'm interested in below. My question is, is there a more standard name for this theorem? I would like to find an additional...

Hey all. I am giving Panhellenic exams this year, and part of my preparation comes from solving previous' years questions. This problem was a complex number based one, in the 2013 Panhellenic exams. It goes as follows: Consider 3 complex numbers, α0,α1 and α2 which belong in the line given by...

Hi, I am trying to find the current of a circuit using mesh analysis so far I have; My voltages V1 = 415 ∠ 90° or 0 + j415 V2 = 415 ∠ 0° or 415 + j0 impedances Z1 = j4 Z2 = j6 My formula is; -V1+Z1*I+Z2*I+V2=0 Which equates to; -0+j415+j4*I+j6*I+415+j0=0 Could...

Why must the gauge group be in a complex representation so that chirality of the fermions is respected? thanks

This problem has been on my mind for a while. ---------- **Problem:** Show that **if** \begin{equation} |z_1+z_2+\dots+z_n| = |z_1| + |z_2| + \dots + |z_n| \end{equation} **then** $z_k/z_{\ell} \ge 0$ for any integers $k$ and $\ell$, $1 \leq k, \ell \leq n,$ for which $z_{\ell} \ne 0.$...

I need to prove that the complex power series $\sum\limits_{n=0}^{\infty}a_nz^n$ converges uniformly on the compact disc $|z| \leq r|z_0|,$ assuming that the series converges for some $z_0 \neq 0.$ *I know that the series converges absolutely for every $z,$ such that $|z|<|z_0|.$ Since...

Matrix A: 0 -6 10 -2 12 -20 -1 6 -10 I got the eigenvalues of: 0, 1+i, and 1-i. I can find the eigenvector of the eigenvalue 0, but for the complex eigenvalues, I keep on getting the reduced row echelon form of: 1 0 0 | 0 0 1 0 | 0 0 0 1 | 0 So, how do I find the nonzero eigenvectors of the...

For example, if someone with an architectural modeling software designed a beautiful mansion or other type of intricate and ornate structure, is there some equation in the computer or some type of mathematical structure to what was designed? Are there potential mathematical blueprints for all...

Do I have the right idea? I'm not getting what is in the solutions manual but it's been wrong on past chapter and I'm beyond frustration.

Homework Statement Here is my equation that I want to find theta angle Homework EquationsThe Attempt at a Solution I try to set different value of cos (theta) to find theta but it failed , I want to know the main solving strategy Thanks

Homework Statement Find the solutions to z^{\frac{3}{4}}=\sqrt{6}+\sqrt{2}i Homework Equations de Moivre's theorem The Attempt at a Solution z^{\frac{3}{4}}=2\sqrt{2}e^{\frac{\pi i}{6}}=2\sqrt{2}e^{\frac{\pi i}{6}+2k\pi}=2\sqrt{2}e^{\frac{\pi +12k\pi}{6}i} z=4e^{\frac{4}{3}{\frac{\pi...

Hi PF! I am trying to run the following plot: k = .001; figure; hold on [X,Y]=meshgrid(-4:0.01:4); a = 5.56*10^14; b = .15/(2*.143*10^(-6)); for n = 1:8 k = k*2^(n-1); Z = a./(X.^2+Y.^2).*exp(b.*(X-sqrt(X.^2+Y.^2)))-k; contour3(X,Y,Z) end which works great if a = b = 1. But now...

I've just encountered the following theorem : If T is a linear operator in a complex vector space V then if < v , Tv > =0 for all v in V then T=0 But the theorem doesn't hold in real 2-D vector space as the operator could be the operator that rotates any vector by 90 degrees. My question...

Hi everyone, I need a little bit of help with an optimization problem and finding the critical numbers. The question is a follows: Question: Between 0°C and 30°C, the volume V ( in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula: V = 999.87 −...

Homework Statement In the circuit shown, R1 = 0.810 Ω, R2 = 8.10 Ω, R3 = 81.0 Ω, and R0 = 810 Ω. See attachment Calculate the equivalent resistance of the circuit when a 7.70 V power supply is connected between points A and C. Calculate the current through R0 and R1 Homework...

Geologists Climb Into Iceland Volcano, Come Out With Stunning Images http://news.yahoo.com/geologists-climb-iceland-volcano-come-stunning-images-132015005.html Talk about a hot job. I hope they get samples for isotopic analysis. There are "small vents of blue sulfur-dioxide gas rise from the...

Homework Statement For ##|z-a|<r## let ##f(z)=\sum_{n=0}^{\infty}a_n (z-a)^n##. Let ##g(z)=\sum_{n=0}^{\infty}b_n(z-a)^n##. Assume ##g(z)## is nonzero for ##|z-a|<r##. Then ##b_0## is not zero. Define ##c_0=a_0/b_0## and, inductively for ##n>0##, define $$ c_n=(a_n - \sum_{j=0}^{n-1} c_j...

Homework Statement I have to prove that I(a,b)=\int_{-\infty}^{+\infty} exp(-ax^2+bx)dx=\sqrt{\frac{\pi}{a}}exp(b^2/4a) where a,b\in\mathbb{C}. I have already shown that I(a,0)=\sqrt{\frac{\pi}{a}}. Now I am supposed to find a relation between I(a,0) and \int_{-\infty}^{+\infty}...

Homework Statement Let f be a function with a power series representation on a disk, say D(0,1). In each case, use the given information to identify the function. Is it unique? (a) f(1/n)=4 for n=1,2,\dots (b) f(i/n)=-\frac{1}{n^2} for n=1,2,\dots A side question: Is corollary 1 from my...

Hi, I need to plot the last function of this: But I don't know how to generate the sum. I know the for loop is totally wrong, but I can't go any further. This is what I have: Can someone fix the summation loop part for me? Thanks in advance

The configuration and dimensions of any experiment are important in determining wave amplitudes. Then why are the orientations of complex waves not considered when they are added? For example in two dimensions; To find a resulting wave at a point P1 from two paths R1 & R2 we have...

This really isn't a homework question but I wasn't sure where to post it. I was watching a video by numberphile about complex numbers and the professer being interviewed said the most important thing about complex numbers is that they help bring algebra and geometry together. What did he mean by...

Homework Statement Given an integer n and an angle θ let Sn(θ) = ∑(eikθ) from k=-n to k=n And show that this sum = sinα / sinβ Homework Equations Sum from 0 to n of xk is (xk+1-1)/(x-1) The Attempt at a Solution The series can be rewritten by taking out a factor of e-iθ as e-iθ∑(eiθ)k from...

Homework Statement Give an example of a power series with [itex]R=1[\itex] that converges uniformly for [itex]|z|\le 1[\itex], but such that its derived series converges nowhere for [itex]|z=1|[\itex]. Homework Equations R is the radius of convergence and the derived series is the term by term...

Homework Statement Prove that \lim_{z\rightarrow z_0} Re\hspace{1mm}z = Re\hspace{1mm} z_0 Homework Equations It is specifically mentioned in the text that the epsilon-delta relation should be used, |f(z)-\omega_0| < \epsilon\hspace{3mm}\text{whenever}\hspace{3mm}0<|z-z_0|<\delta . Where...

Possibly a difficult question, but I've never found a discussion on the topic. Thanks

I am reading Kristopher Tapp's book: Matrix Groups for Undergraduates. I am currently focussed on and studying Section 1 in Chapter2, namely: "1. Complex Matrices as Real Matrices".I need help in fully understanding the proof of Tapp's Proposition 2.2. Proposition 2.2 and its proof read as...

I am reading Kristopher Tapp's book: Matrix Groups for Undergraduates. I am currently focussed on and studying Section 1 in Chapter2, namely: "1. Complex Matrices as Real Matrices".I need help in fully understanding what Tapp is saying in this section regarding the function $$ \rho_n \ : \...

Homework Statement y=[(1+y^2)^1.5]/[2(y+sqrt 3)^2]; solve for y Homework Equations see above The Attempt at a Solution I tried to use algebra to solve it, but I can't. The textbook says it can be solved numerically or by iteration. By numberically I think it means algebraically. But I don't...

Homework Statement Find the largest set D on which f(z) is analytic and find its derivative. (If a branch is not specified, use the principal branch.) f(z) = Log(iz+1) / (z^2+2z+5) Homework EquationsThe Attempt at a Solution Not sure how to even attempt this solutions but I wrote down that...

Homework Statement [moderator note: Image inserted to be visible in problem statement] Homework EquationsThe Attempt at a Solution My friend and I are trying to figure out how this works. This is the questions and the solution manual. We understand where the real power comes from but not at...

Homework Statement Find the maximum value of f(z) = exp(z) over | z - (1 + i) | ≤ 1 Homework Equations |f(z)| yields the maximum value The Attempt at a Solution f(z) = exp(x) ( cosy + i siny) Unfortunately that's all I've got. I've seen examples with polynomials, but not with trigonometric...

Hi, I am currently teaching myself complex analysis (using Stein and Shakarchi) and wondered if someone can guide me with this: Find all the complex numbers z∈ C such that f(z)=z cos (z ̅). [z ̅ is z-bar, the complex conjugate). Thanks!

Homework Statement What is the amplitude and phase of the complex function? f(t) = (1-2i)e^(iwt) Homework Equations None/unknown Normal Polar Form = Real*e^imaginary i = e^pi/2*i The Attempt at a Solution [/B]I am trying to bring this into a normal polar form to easily see the phase and...

*How can I finish off the "only if" direction? I am just unable to prove the only if direction! Using the induction hypothesis and the triangle inequality is confusing me for some reason.* Show that \begin{equation} |z_1+z_2+\dots+z_n| = |z_1| + |z_2| + \dots + |z_n| \end{equation} if and only...

1)If a= cosα + i sinα and the equation az2 + az +1 =0 has a pure imaginary root, then tanα=? 2) cosα+isinα=eiα , quadratic formula 3) What i tried to do was,i put a constant real number and tried to solve it and used demoivres theorem, although the answer is getting weirder and weirder.

Recommend a self study book for linear algebra with complex numbers

Homework Statement Find lim_{x->- \infty} \; \frac{(x^6+8)^{1/3}}{4x^2+(3x^4+1)^{1/2}} Homework Equations N/A The Attempt at a Solution Factoring out \frac {(-x^6)^{1/3}}{-x^2} leaves me with \frac{(-1-8x^{-6})}{-4+(3+x^{-4})^{1/2 }} Taking the limit at infinity gives me...

I've been trying to figure out a way to get an approximation to a complex DiffEQ. dx/dt = c1 / (c2 + c3*x*t) Does anyone have any input on wether this problem can be approximated? Thank you.

Homework Statement This isn't a standard homework problem. We were asked to do research and to find a theorem of the form: If something about the partial derivatives of u and v is true then the implication is ##D(u,v)## at ##(x_0,y_0)## exists from ##R^2## to ##R^2##Homework EquationsThe...

Homework Statement Find the principle argument Arg z when z = (sqrt(3) - i)^6 Homework EquationsThe Attempt at a Solution I'm sorry to say that I'm not sure how to solve this problem. It's my understanding that what this question is basically asking me to do is find theta such that...

Homework Statement show that the following functions are differentiable everywhere and then also find f'(z) and f''(z). (a) f(z) = iz + 2 so f(z) = ix -y +2 then u(x,y) = 2-y, v(x,y) = x Homework Equations z=x+iy z=u(x,y) +iv(x,y) Cauchy-Riemann conditions says is differentiable everywhere...

Homework Statement Homework EquationsThe Attempt at a Solution I assumed there to be two supernodes. The first one was between V1 and V2. The second supernode was between V2 and V3. This is what i tried and i am not getting the right answers. Please can someone help me out! Apologies...

I'm just starting this, but what would the complex conjugate of Ψ(x,t) in the equation : |Ψ(x,t)|^2= Ψ(x,t)* Ψ(x,t) be.. Let's just say, for example, that x is 4 and t is 9... Please help if you can.. Could you please help me out with the steps to completing this, because I really want to...

Homework Statement ((1-i)/(sqrt2))^42 express in x+iy form Homework Equations z1/z1=(r1/r2)e^(i(theta1-theta2)) The Attempt at a Solution Ive found that (1-i) has r=sqrt2 so since r is sqrt2 and x=1 y=-1 so the angle is 7pi/4 so then I have (sqrt2e^(-i7pi/4)/sqrt2)^42 now from here is where I...