Recent content by annawells

ohhhh :( okay I will think about it! does anything make a difference that K contains complex numbers no?

yessssss! :) :D thanks a million!

okay. sooo, the argument is that: If z is constructible then its minimal polynomial has a degree which is a power of 2. For z = 2^(1/p), z has minimal polynomial i(z^p)-2, which has degree p (which is obviously not a power of 2). So z is not constructible. Is it obvious to say that...

okay thanks! is there some lemma/theorem that states that these numbers are not constructable?? for either pth root of 2, or cube root of p?!

Thanks, that makes sense! So you are looking at all the pth roots for p prime yeh? and each extension has a degree of 2? so with some application of towers law (which says that for M<N<L, [L:M] = [L:N]*[N:M] ) we get that its infinite. Instead of adding all the elements pth root of 2, would...

Homework Statement Let K be the subfield of all constructible numbers in C Let A be the subfield of all algebraic numbers in C Is the field extension A:K finite? The Attempt at a Solution I don't know where to start! I have read and understood proofs that all constructible numbers...

thanks a million!

okay, thanks a lot! i didnt know that thing about g(z)/z , thanks. but then, what is the residue at the singularity? its the coefficient of the "1/z" term, and here that looks to be g(z) though its not exactly a coefficient,its a series!

Thanks, I was wondering how people made the functions look nice on here! i have often found answers here, but never posted before; thanks for the welcome :-) well, when z --> 0, we have the zf(z)--> -1 i am not sure what that says about the nature of a function? if 0 were a simple pole...

Thanks for the idea. I am not quite sure how to pursue it. To show it is an essential singularity, don't i need to "produce" the laurent series, or at least show that it has infinite negative terms? I don't know how to break up the fraction to do that!? maybe this is more of a problem with my...

Homework Statement The following function has a singularity at z=0 (e^z)/(1 - (e^z)) decide if its removable/a pole/essential, and determine the residue The Attempt at a Solution I played with the function and saw it can be re-written as: -1 /(z + z^2/2! + z^3/3! +...) In this...