Recent content by nugget

Hey thanks for the help guys, I see what you mean, much neater! cheers

Homework Statement Find a formula for: \int1/(z-a)m(z-b)ndz around a ball of radius R, centred at z0 where |a| < R < |b| and m,n\inN. Homework Equations Not sure which equations to use, a cauchy integral formula maybe...? The Attempt at a Solution I've attempted to...

Hey thanks for the advice! I was already pretty happy with part (a) the result looks quite similar for part b) are you able to tell me if i should end up with this? : (1/2i)*(j=0\sum\infty [(i^j) - ((-i)^j)]/(z^j+1) I feel good about using the example you gave but would love to know for...

1. Homework Statement For f(z) = 1/(1+z^2) a) find the taylor series centred at the origin and the radius of convergence. b)find the laurent series for the annulus centred at the origin with inner radius given by the r.o.c. from part a), and an arbitrarily large outer radius. 2...

I got part a) I'm fairly confident that the answer is f(z) = (\frac{1}{2})0\sum\infty ((zj) + (-z)j)/(ij) (sum from 0 to infinity) But don't understand how to do laurent series... I think I need to do it for the annulus centered at the origin with radius 1, and then again for the annulus...

Hey Jackmell, could you please explain how you would show that the magnitudes of some of the things in this integral are equal to one? i understand for eit but not for eiR2cos(2t)

Homework Statement Suppose f is an entire function, satisfying f(z + a) = f(z) = f(z + b), for all z \in C; where a; b are nonzero, distinct complex numbers. Prove that f is constant. Homework Equations Loville's theorem: if f is bounded & entire, then f is constant. The...

and now I'm trying to multiply polynomials from the galois field by polynomials from C, and still ending up in C. perhaps their dodgy proof is the right way?

I don't see how there could be a codeword in C that can't be formed under cyclic shifts. I have a theorem in my notes regarding cyclic codes, and it is the only one given so I assume I need to use it: C is Cyclic if and only if it is an ideal of GF(q)[x]/<x^{n}-1> so I need to show that every...

It makes sense that because the sums of the bits must be even, then d cannot equal an odd number. So I suppose that is sound enough logic to say it is an MDS code, because then the minimum distance is always 2! nice Cyclic codes are those where each element can be formed via cyclic shifting...

Homework Statement Suppose n\leq2 Let C be the code consisting of all binary strings of length n in which the sum of the bits is even. Is C and MDS code? is C a cyclic code? Homework Equations An MDS code is one where the codewords are separated by a maximum number of bits d. MDS codes obey...

Hey, regarding that deg(g)=0 bit, I guess I just assumed that a constant would be a unit in I. This would only be the case if R was a field, right? Now I'm really confused for this question too; don't know how to prove the division algorithm, let alone for an integral domain. I think I...

Homework Statement Suppose R is an integral domain and I is a principal ideal in R[x], and I \neq {0} a) Show I = <g(x)> for some g(x)\inR[x] that has minimal degree among all non-zero polynomials in I. b) Is it necessarily true that I = <g(x)> for every g(x)\inR[x] that has minimal...

Hey guys, Thanks for your help, but I'm still confused. I have found f(z) = 1/(z+i)(z-i) and I think I've found the partial fractions representation: f(z) = 1/2i(z-i) - 1/2i(z+i) but don't know where to go from here... do I seperately apply taylor series expansion to each of these fractions...?

Homework Statement For f(z) = 1/(1+z^2) a) find the taylor series centred at the origin and the radius of convergence. b)find the laurent series for the annulus centred at the origin with inner radius given by the r.o.c. from part a), and an arbitrarily large outer radius. Homework...