Complex analysis Definition and 784 Threads

Homework Statement Write z^3 + 5 z^2 = z + 3i as two real equations Homework Equations z=a+bi? The Attempt at a Solution I've been just playing around with this. I expanded, grouped the real and imaginary parts. I'm really just think I'm groping around desperately in the dark. I think...

I am studying signal processing. I took a class last year but don't have a class now (it is very part time) and would like to do some self study. I did alright in my last class but feel that my appreciation of it would have been greater if I had a better background in complex analysis. Could...

Hello!, I was studing the conformal maps in complex analysis, I don't understand this definition: Definition: A map f:A\rightarrow\mathbb{C} is called conformal at z_0 if there exist a \theta\in[0,2\pi] and r>0 such that for any curve \gamma(t) which is differentiable at t=0, for which...

If Pdx+Qdy is locally exact in R`,prove that \intPdx+Qdy=0 for every cycle Y-0 in R`.

I read the reviews that it's one of the classics in this topic, I wonder does someone know why AMS publishing stopped printing the book (im reffering to the three volumes in one book), especially when the book was published in 2005, i know that it's not profitable but for classic book i would...

Homework Statement f(z) = (z+1)/(z-1) What are the images of the x and y axes under f? At what angle do the images intersect? Homework Equations z = x + iy The Attempt at a Solution This is actually a 4 part question and this is the part I don't understand at all really. The...

I have a homework question that reads: Represent the following rational functions as sums of elementary fractions and find the primitive functions ( indefinite integrals ); (a) f(z)=z-2/z^2+1 But my confusion arrises when I read sums of elementary fractions. I think what the question is...

Homework Statement f:Complex Plane ->Complex Plane by f(z) = (e^z - z^e)/(z^3-1) continuous? (Hint: it has more than one discontinuity.) The Attempt at a Solution My attempt at a solution was thus, initially I expanded z^3 and tried to find where it equaled 1. That wasn't...

So my teacher explained what holomorphic functions were today. But it did not make much sense. As I am attempting to do my homework, I realized that I still don't really know what a Holomorphic function is, let alone how to show that one is. The questions looks like this: show that...

Homework Statement 1) \frac{e^{z}-1}{z} Locate the isolated singularity of the function and tell what kind of singularity it is. 2) \frac{1}{1 - cos(z)} z_0 = 0 find the laurant series for the given function about the indicated point. Also, give the residue of the function at the...

Homework Statement Evaluate \oint_C \f(z) \, dz where C is the unit circle at the origin, and f(z) is given by the following: A. e^{z}^{2} (the z2 is suppose to be z squared) B. 1/(z^{2}-4) Homework Equations The Attempt at a Solution I'm completely confused

Homework Statement Determine where the function f has a derivative, as a function of a complex variable: f(x +iy) = 1/(x+i3y) The Attempt at a Solution I know the cauchy-riemann is not satisfied, so does that simply mean the function is not differentiable anywhere?

Homework Statement 1) Where is f(z)=\frac{sin(z)}{z^{3}+1} differentiable? Analytic? 2) Solve the equation Log(z)=i\frac{3\pi}{2} Homework Equations none really... The Attempt at a Solution For #1 I started out trying to expand this with z=x+iy, but it got extremely messy...

Just wondering, when starting on introductory analysis is it logical to do real analysis before complex variables? My guess is complex analysis uses things from real analysis. I'm doing very basic analysis in calc 2, and not sure if its enough to get by complex.

Homework Statement Let f(z) = \frac{1-iz}{1+iz} and let \mathbb{D} = \{z : |z| < 1 \} . Prove that f is a one-to-one function and f(\mathbb{D}) = \{w : Re(w) > 0 \} . 2. The attempt at a solution I've already shown the first part: Assume f(z_1) = f(z_2) for some z_1, z_2 \in...

Hi all, I'm torn between taking complex analysis or differential geometry at the advanced third year level. Which of these would you consider the easiest to self-learn or the least applicable to the study of theoretical physics? I know that differential geometry shows up in general relativity...

Hi! I am signing up to take my first course in complex analysis this upcoming semester at my university. One of the professors with whom I am interested in taking the class is using Complex Analysis 2nd edition by Bak & Newman and the other one is using Complex Variables & Applications 7th...

Homework Statement Find all solutions to: e^{\tan z} =1, z\in \mathbb{C}Homework Equations z = x+yi \log z = ln|z| + iargz +2\pihi, h\in \mathbb{Z}\log e^{z} = x + iy +2\pihi, h\in \mathbb{Z}Log e^{z} = x + iy The Attempt at a Solution I do not really know how to approach this, I tried to...

Homework Statement Solve cosz = 2i , z\in \mathbb{C} The Attempt at a Solution e^{iz}+e^{-iz} = 4i t=e^{-z} t+t^{-1}=4i \Rightarrow t^{2}-4it+1=0 t = (2 \pm \sqrt{5})i log(e^{-z}) = logt z = x + yi;x,y \in \mathbb{R} log(e^{-z}) = log(e^{-y+ix}) = -y +xi +...

Advice: How do I master complex analysis in 5 weeks? ??! Homework Statement Need to be throughly proficient with th first 7 chapters of saff and snider : fundamentals of complex analysis with engineering applications. Homework Equations egads! there's too many! The Attempt at a...

Is my proof correct for lim_(n-> infty) |z_n| = |z| ? Complex Analysis Homework Statement Show that if lim_{n-> infty} z_n = z then lim_{n-> infty} |z_n| = |z| Homework Equations The Attempt at a Solution Is this correct: lim_{n-> infty} |z_n| = |z| iff Assume...

This really is a question on complex analysis but is about Polchinski's introduction to worlsdheet physics, so I am sure people here will answer this easily. I know it is a very basic question. Polchinski considers a field which is analytic and then says that because of this, one may write it...

Homework Statement the question can be ignored - it involves laplace and Z transforms of RLC ckts. Vc(s) = 0.2 ----------------- s^2 + 0.2s + 1 find the partial fraction equivalent such that it is : -j(0.1005) + j (0.1005) --------------...

I'm currently doing a course in complex analysis and we're using fundamentals of complex analysis, by saff and snider. https://www.amazon.com/dp/0139078746/?tag=pfamazon01-20 And Our problem sets are from the questions at the end of the chapters. I'm finding these questions incredibly hard...

I suppose this is the proper place for this question:) I am learning about conformal field theories and have a question about poles of order > 1. If a conformal transformation acts as z \rightarrow f(z), f(z) must be both invertable and well-defined globally. I want to show that...

Hi could please let me know the Dirichlet's theorem(Complex analysis) ,statement atleast... as stated in John B Comway's book if possible ...I don't have the textbook and its urgent that's why...thank You

Oh god, so confused and panicked today:cry: I know this is a very basic question, but, givin the function 1/(z-w)^4 does this have one pole of order 4, or possibly 4 poles of order 1...? Also, could you please clarify, ''to get the zero's of a function, set the numerator = 0'' ''to...

Hello guys, Could someone reccomend me a complex analysis textbook? My class is currently using Stewart but i heard this is not such a good text...

1) Let U be a subset of C s.t U is open and connected and let f bea holomorphic function on U s.t. for every z in U, |f(z)| = 1, ie takes takes all points in U to the boundary of the unit circle. Prove that f is constant. Pf. Suppose f is not constant. Then we can find a w s.t. f'(w) is...

Homework Statement Prove that if a function f:c->c is analytic and lim as z to infinity of f(z)/z = 0 that f is constant. Homework Equations Cauchy Integral Formula for the first derivative (want to show this is 0 ie: constant) f prime (z) = 1/(2ipi)*Integral over alpha (circle radius...

Can anyone give me some advice on how to solve this problem? in the reflection principle if f(x) is pure imaginary then the conjugate of f(z)=-f(z*) where z* is the complex conjugate of z. Any advice on where to start? thanks

Can anyone give me some advice on how to solve this problem? in the reflection principle if f(x) is pure imaginary then the conjugate of f(z)=-f(z*) where z* is the complex conjugate of z. Any advice on where to start? thanks

Hello! I am studing for my Complex Analysis exam and solving the exercises for Residues given by the professor. The problem is that for some exercises I get to a solution different from the one of the professor :bugeye:, and I am not sure that the mistake is in my calculations. I would...

Homework Statement 1. Evaluate the following integrals using residues: a) \int _0 ^{\infty} \frac{x^{1/4}}{1 + x^3}dx b) \int _{-\infty} ^{\infty} \frac{\cos (x)}{1 + x^4}dx c) \int _0 ^{\infty} \frac{dx}{p(x)} where p(x) is a poly. with no zeros on {x > 0} d) \int _{-\infty}...

Homework Statement 1. Suppose that f(z) is holomorphic in C and that |f(z)| < M|z|n for |z| > R, where M, R > 0. Show that f(z) is a polynomial of degree at most n. 2. Let f(z) be a holomorphic function on a disk |z| < r and suppose that f(z)2 is a polynomial. Is f(z) a polynomial? Why...

Homework Statement Show that \frac{\sin (az)}{\sin (\pi z)} = \frac{2}{\pi} \sum_{n=1}^{+\infty} (-1)^n \frac{n \sin (an)}{z^2 - n^2} for all a such that - \pi < a < \pi Homework Equations None really, we have similar expansions for \pi cot (\pi z) and \pi / \sin (\pi z) , this...

Some hints/help woudl be greatly appreciated! Let I(r) = integral over gamma of (e^iz)/z where gamma: [0,pi] -> C is defined by gamma(t) = re^it. Show that lim r -> infinity of I(r) = 0.

Can anyone help with these problems 1). use def. delta epsilon proof to prove lim(z goes to z0) Re(z)=Re(z0) This is what I did |Re(z)-Re(z0)| = |x-x0| < epsilon then |z-z0|=|x-iy-x0-iy0|=|x-x0+i(y-y0)|<=|x-x0|+|y-y0|=epsilon + |y-y0| = delta My question is doesn't this delta have to...

Homework Statement Is there a Laurent Series for Log(z) in the Annulus 0<|z|<1? Homework Equations Go here for the Theorem. It is theorem 7.8: www.math.fullerton.edu/mathews/c2003/LaurentSeriesMod.html[/URL] (copy and paste the link below if you are having problems. Exclude the "[url]" in...

I need a book that's semi-introductory (advanced undergrad to beginning graduate level, if possible) on complex analysis, particularly one that covers power series well, but should be fairly general. I currently have "elementary real and complex analysis" by Georgi Shilov and while it's not...

Preface:The best way I've been taught how to prove that a force is conservative is to take the curl of the force and show that it is equal to zero. That's pretty quick, but after studying for a complex analysis midterm this idea struck my mind. I'm not a master of complex analysis, so there...

Hello everyone, I am trying to solve this follow problem, but don't quite know how to go about getting Arg(z). z = 6 / (1 + 4i) I got that lzl is sqrt((6/17)^2+(-24/17)^2) but am stuck with finding Arg(z). It told me to recall that -pi < Arg(z) <= pi Can you guys teach me how to go...

So my professor threw in what he called an extra 'hard' question for a practice test. So naturally I have a question about it. It relates to the Maximum Modulus Principle: a) Let p(z) = a_0 + a_1 z + a_2 z^2 + ... and let M = max |p(z)| on |z|=1. Show that |a_i|< M for i = 0,1,2. b)...

for our project in calculus, I am doing a presentation on the basics of complex analysis. Somewhere along there I need to tackle the question: what are the applications of complex analysis? Are there any application problems that I can give that involve basic derivatives/integrals of complex...

Hi. So I was reading through "Elementary Real and Complex Analysis" by Georgi E. Shilov (reading the first chapter on Real Numbers and all that "simple" stuff like the field axioms, a bit of set stuff, etc.). Anyways, so while I was reading, I ran into something I couldn't understand... the...

I have two questions on complex integration, and I do not know how to solve them. Please help if you can. Thanks 1. Evaluate the following principal value integral using an appropriate contour. Integration of (integral goes from 0 to infinity) : (x)^a-1/1-x^2, 0<a<1. 2.Using contour...

Let C be a simple closed curve. Show that the area enclosed by C is given by 1/2i * integral of conjugate of z over the curve C with respect to z. the hint says: use polar coordinates i can prove it for a circle, but i am not sure how to extend it to prove it for any given closed curve

Suppose that f is analytic on a domain D, which contains a simple closed curve lambda and the inside of lambda. If |f| is constant on lambda, then either f is constant or f has a zero inside lambda ... i am supposed to use maximum/modulus principle to prove it ... here is my take: if f...

Verify that the linear fractional transformation T(z) = (z2 - z1) / (z - z1) maps z1 to infinity, z2 to 1 and infinity to zero. ^^^ so for problems like these, do I just plug in z1, z2 and infinity in the eqn given for T(z) and see what value they give? in this case, do i assume 1/ 0 is...

(changes in arg h (z) as z traverses lambda)/(2pi) = # of zeroes of h inside lambda + # of holes of h inside lambda now the doubt i have is what happens when the change i get in h (z) is say 9 pi/2 ... because then i would have a 2.5 on left side of the eqn ... so do i round it up and...