Complex analysis Definition and 784 Threads

find a one-to-one analytic function that maps the domain {} to upper half plane etc ... for questions like these, do we just have to be blessed with good intuition or there are actually sound mathematical ways to come up with one-to-one analytic functions that satisfy the given requirement...

Hi again. Can somebody help me out with this question? "\int_{C_1(0)} \frac {e^{z^n + z^{n-1}+...+ z + 1}} {e^{z^2}} \,dz Where C_r(p) is a circle with centre p and radius r, traced anticlockwise." I'd be guessing that you have to compare this integral with the Cauchy integral formula...

Suppose you have a Meromorphic function f(z) that has a zero at some point in the complex plane. Suppose you create two parallel contours Y1 and Y2 that are parallel and infinitely close to each other yet still contains the zero (the contours are infinitely close to the zero but don't run...

so .. if f (z) = u + iv is analytic on D, then u and v are harmonic on D... now ... if f (z) never vanishes on the domain ... then show log |f (z)| is harmonic on the domain ... Recall: harmonic means second partial derivative of f with respect to x + second partial derivative of f with...

Consider the function: g(z(t)) = i*f '(c+it)/(f(c+it) - a) Where {-d <= t < d} If we let z = c+it By change of variables don't we get: Line integral of g(z(t)) = i ln[f(c+it) - a] evaluated from t = - d to t = d? note: ln is the natural log. Inquisitively, Edwin...

hi, I'm wondering if someone can help me out with this question: "What are the first two non-zero terms of the Taylor series f(z) = \frac {sin(z)} {1 - z^4} expanded about z = 0. (Don't use any differentiation. Just cross multiply and do mental arithmetic)" I know the formula for...

I think I have misunderstood one of the theorems in complex analysis (k reperesents the order of the derivative) Theorem: Suppose f is analytic on a domain D and, further, at some point z0 subset of D, f (k) (z0) = 0. Then f(z) = 0 for all z subset of D ... Is the theorem basically...

Here's my question: Let f and g be analytic inside and on the smple loop \Gamma. Prove that if f(z)=g(z) for all z on \Gamma, then f(z)=g(z) for all z inside \Gamma. Don't really know where to start on this one. This comes from the section 'Cauchy's Integral Formula'.

I'm glad to see that the physics forum website is back online. Suppose you have a function with double poles somewhere on the complex plane. Are there complex analysis techniques that can be used to split the double pole into two single isolated poles? Some example functions might be...

I'm struggling with this question right now: Let the complex velocity potential \Omega(z) be defined implicitly by z = \Omega + e^{\Omega} Show that this map corresponds to (some kind of fluid flow, shown in a diagram, not important). For background, \Omega = \Phi + i\Psi...

Consider a domain D and f:D-->\mathbb{C} a holomorphic function and C a contractible Jordan path contained in D and z1, z2, two points in the interior of C. Evaluate \int_C \frac{f(z)}{(z-z_1)(z-z_2)}dz What happens as z_1 \rightarrow z_2? I have found that \int_C...

Prove that if wz = 0, then w = 0 or z = 0. w and z are two complex numbers. I said that w = a + bi and z = c + di and set wz = 0. I got down to c(a+b) = d(b-a), but don't know where to go from here. I'm trying to teach myself complex analysis, anyone know any good sources? I took the 3...

Suppose you have a unit circle in the complex plane e^{it}, -\infty \leq t \leq \infty. The contour will wind around forever, so at all points in the contour, there are an infinite amount of possible winding numbers, although they are all multiples of 2pi with a well defined contour boundry...

hi there im confused with this question.. Integrate 1) Sin(1/z) dz and 2) Z sin (1/Z^3) where Z is any complex number., over C which is a circle of radius 1 centred at 0 i tried using the cauchy integral formula and stuff but somehow the answer always comes infinity...is...

"Let a,b be in R with a>0 and f(x)=ax^3+bx. Let k(x)=[f''(x)]/[1+(f'(x))^2]^(3/2). Find the critical points of k(x) and use the first derivative test to classify them." This seems incredibly quantitative and complicated for an analysis assignment. There must be a theorem of some kind I can...

Hi there, I'm taking this math for physicists course and we're doing some stuff with functions of complex variables (laurent series residue etc), and I"m having a bit of trouble. I'm not so happy with the book we use. It's a great reference book if you know what you're doing already but...

Can someone tell me when explicit use of complex analysis arises in physics? What particular courses? Thanks

complex analysis-- Oscillation/vibration class Hello all, I'm taking a wave/vibration/oscillation class, and we're delving into complex notation for these. One of our assigments dealt with a complex function that we didn't get a whole lot of practice out of in math methods. I've gone back...

As you know complex analysis has provided many useful tools for harmonic analysis. However I think its application to Einstein's theory of relativity is relatively limited. So I tried to modify complex analysis in order to apply it to the theory of relativity more easily in the following...

"Visual Complex Analysis" I have gotten myself wound around the axel regarding something in "Visual Complex Analysis" (Dr. Tristan Needham) that should be easy. On p. 18 (paperback edition), towards the bottom, the result for two rotations about different points has got me stumped. I cannot...

hello all well i am going to slowly research my way into complex analysis and I decided to start with cauchys theorem i hope this is the best part to start with, well anyway it says that if f(z) is analytic and \frac{f(z)}{z-z_{o}} has a simple pole at z_{0} with residue f(z_{o}) then...

Hi PPls okay i have studied calculus and i can easily see its application in many things like calculating volume,areas,rates ..etc. but i want to know what is the application of complex analysis...where does it all find its uses and why one study it??

Hi all,, I have a problems on complex Analysis: Show that the equation z^4 + z + 5 = 0 has no solution in the set { z is a subset of C: modulus of z is less than 1} i tried doing it using Triangle inequality although i got it but i am looking for a better solution...Pls help

I would appreciate if someone could explain Conformal Mapping using Complex Analysis using an example. I get the rough idea but have no clue how complex analysis comes into the picture. Thank You!

This one is pretty involved so mad props to whoever can help me figure it out. I've been thinking about this for more than an hour and it's bugging me. Consider the function f(z) = 1/(sin(pi/z)). It has singular points at z=0 and z=1/n (where n is an integer). However, my book says each...

I was just wondering what exactly complex analysis is, and what type of applications it's study can be applied to. By the way, an excellent discussion/class on differential forms is taking place here , if anyone would be interested in starting a similar type forum on complex analysis, that...

need some urgent help with basic complex analysis (no proofs) This forum is probably more appropriate. please forgive me for double posting. Can someone give me examples of the following? (no proofs needed) (C is the complex set) 1. a non-zero complex number z such that Arg(z^2) is NOT...

i know it's supposed to be a simple question. frustrating because it is not coming to me. just want a hint. question is: how do you write 1 + cos(theta) + cos (2*theta) + cos(3*theta)... cos(n*theta) using the fact that (z^(n+1) -1) / (z^(n) -1) = 1 + z + z^(2) +... + z^(n) thanks in...

Cauchy integral question The question calls for finding the integral of dz/((z-i)(z+1)) (C:|z-i|=1) I can't figure out how to do this for (C:|z-i|=1). How does this differ from, say, (C: |z|=2) Regards

Here's a problem I ran into in complex analysis. Given z = x + iy and w = u + iv, I need to find all w such that w² = z. It reduces to solving this system: x = u² - v² y = 2uv My professor mentioned that we should try to deal with the problem in at least two cases: y = 0, and y does not...

Hi people, I'm Joseph, 17, English studying European Baccalaureate. I was wondering if anyone here could recommend for me a good introductory book on Complex Analysis that requires only an understanding of the complex numbers you would cover in High School Maths. Maybe something...

Anyone know how to find a sum of a function using the poisson summation formula and the Fourier transform. Thanks! --yxgao

More "Complex" Complex Analysis I have another problem that has eluded me for days and I'm sure I'm close. If anyone can help, please nudge me in the right direction. Consider the mapping w = u + iv = 1/z, where z = x + iy. Show that the region between the curves v = -1 and v = 0 maps into...

I am having trouble with the following question, any help would be blinding. Find the value of ther derivative of: (z - i)/(z + i) at i. I tried to use the fact that f'(z0) = lim z->z0 [f(z) - f(z0)]/z - z0. I also tried using the fact that z = x + iy and rationalising the denominator...