Recent content by FanofAFan

Awesome, I figured it out, thanks

Homework Statement number of ring homomorphisms from Z \rightarrow Z? Homework Equations The Attempt at a Solution According to this information on ring homo, There is no ring homomorphism Zn → Z for n > 1. But I guess that doesn't hold for when n = 1, any ideas

Ok, I know -1/2 had to be a pole but I meant e^(ipi)/2 which is also -1/2 and also when i try to find the residue at that point I end up getting constant/zero... ie res at -1/2 = (-1/2)^3/24(-1/2+1/2)^2 is that wrong?

Homework Statement find the pole and it's order for f(z) = \frac{z^3}{(2z+1)^3} Homework Equations \frac{1}{(2z+1)^3} as \frac{1}{8(z+1/2)^3} The Attempt at a Solution poles at z = -1/2, \frac{e^(i*\pi)}{2}, and \frac{e^(-i*\pi)}{2}

Homework Statement Give an example of a commutative ring R with a 1 and nonzero prime ideal P of R such that P = P2 Homework Equations The Attempt at a Solution Letting R be an integral domain and look at the ideal 0xR in RxR. is all i got but not sure how to show this or what to...

So Let M/I be a maximal ideal of R/I and R is commutative ring, So we need to show that M is maximal ideal of R, let H be an ideal of R such that M \subseteq H \subseteq R and every ideal is a sub-ring, then H is a sub ring of R. Therefore M is a sub-ring of H \subseteq R, H is normal to I...

Homework Statement R is a commutative ring, and normal to I, let M/I be a maximal ideal of R/I. Prove that M is a maximal ideal of R?Homework Equations The Attempt at a Solution Not sure where to begin, but I think since we know R is commutative then we can say R/I is commutative and since M/I...

Is it Maclaurin series for exponental... so 1 + e^(2i pi/3) z = cos(2 pi/3) + i sin(2 pi/3) z + and so on... right?

Si it is 1+e2pi*i/3z + e4pi*i/3z2 + e6pi*i/3z3 + .. + ek(2pi*i/3)zk

Not sure where to begin, thought I'd get some type of hint, but I figured let z = x +iy and change the series to sin(2pi/3) + x sin(4pi/3) + iy sin(4pi/3) + x2 sin(6pi/3) - y2 sin(6pi/3) + 2ixy sin(6pi/3) +...+ and maybe separate the series in real and imaginary parts, I'm completely off

Homework Statement Find the sum in |z| < 1 of the series sin(\frac{2\pi}{3}) + z sin(\frac{4\pi}{3}) + z2 sin(\frac{6\pi}{3}) + ... + zk sin(k\frac{2\pi}{3}) + ...Homework Equations \sum n =1 to \infty (e2pi*i/3z)n = 1 + \sum n =1 to \infty (e2pi*i/3z)n The Attempt at a Solution

so i got the integral of M1(z-z)M1-1/(z-z1)M1 + ... + etc which by my attempt in wolfram is M1/(z-z1) http://www.wolframalpha.com/input/?i=y%28x-1%29^%28y-1%29+%2F%28x-1%29^y

wait the integral is M1/(z-z1)+M2/(z-z2)...+Mn/(z-zn)...

M1(z-z1)M1-1 + M2(z-z2)M2-1 +...+Mn(z-zn)Mn-1 and the integral of that is just (z-z1)M1 + (z-z2)M2 .. etc?

P'(z) = M1(z-z1)M1-1(z-z2)M2...(z-zn)Mn +M2(z-z1)M1(z-z2)M2-1...(z-zn)Mn +...+ Mn(z-z1)M1(z-z2)M2...(z-zn)Mn-1