Complex variables, maximum value

Thread starter babyrudin
Start date Mar 18, 2008
Tags

Complex Complex variables Maximum Value Variables

Mar 18, 2008

babyrudin

Homework Equations

Let w \in C be a fixed complex number with |w|<1. Let
f(z)=\frac{z-w}{1-\bar{w}z}.
Calculate its maximum value in the region |z| \leq 1.

The Attempt at a Solution

How should I approach this? Not sure if maximum modulus principle is of much help.

Physics news on Phys.org

Electric signals reveal magnetic spin waves, hinting at faster computing
Topological insulator maintains quantum spin Hall effect at higher temperatures
Nuclear clock technology enables unprecedented investigation of fine-structure constant stability

Mar 19, 2008

babyrudin

Any idea on this?

Thread 'Complex Numbers (Laurent Series)'

see attached.

View full post »

Thread 'Necessary criterion for expressing f(a + b)'

It's easy to see that any polynomial is function of that class. Also it seems that composition of exponent and polynomial is good as well. G_f(a, b) should be equal G_f(b, a) as the f(a+b) is symmetrical. Does anyone have information about this or at least related to it?

View full post »

Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...

View full post »