Unity Definition and 127 Threads

I am typing up a latex document and I need to find roots of unity, lots of them, for numbers like say 42. I was just wondering if anyone knew of a database that had this stuff on hand rather than having to do it all by hand and worrying about having made some stupid algebra error.

Homework Statement From contemporary abstract algebra : http://gyazo.com/08def13b62b0512a23505811bcc1e37e Homework Equations "A subring A of a ring R is called a (two-sided) ideal of R if for every r in R and every a in A both ra and ar are in A." So I know that since A and B are ideals of...

Good afternoon. Here is the problem: Show that if $R$ is a ring with unity and $N$ is an ideal of $R$ such that $N \neq R$, then $R/N$ is a ring with unity. My answer: Consider the homomorphism $\phi: R \to R/N$. Given $r \in R$ we have that $\phi(r) = r + N = \phi(1 \cdot r) = \phi(r \cdot 1)...

i'm trying to prove the sum of nth roots of unity = 0, but I don't really know how to proceed: suppose z^n = 1 where z ε ℂ, suppose the roots of unity for z are 1, ω, ω^2, ω^3 ... ω^n the sum of these would be S = 1 + ω, ω^w, ω^3 +...+ ω^(n-1) + ω^n from here I had an idea to do some...

I have some math problems What is the solution to this equation : z dash(complex conjugate) = z^3 Z is complex number I try to multiply both sides by Z in the left i get Z dash Z => |Z| but i don't see the solution ---- P is primitive 9th root of unity. Calculate the sum 1 + 2P...

Challenge Problem $1,a_1,a_2,a_3, \cdots ,a_{n-1}$ are the $n^{\text{th}}$ roots of unity. Find the value of i) $(1-a_1)(1-a_2)(1-a_3) \cdots (1-a_{n-1})$ ii)$\displaystyle \frac{1}{2-a_1}+\frac{1}{2-a_2}+\frac{1}{2-a_3}+\cdots +\frac{1}{2-a_{n-1}}$

Hello, Please help in solving the four set of problems, i will be very happy explaining comment as really want to understand. The problem will spread to the extent of understanding preduduschey. 1 Problems: The set M, M = {e^(j*2*pi*k/n) , k= 0,1,2...n-1} denotes the set of the nth...

i have attached a bode plot and the opamp dc second order lpf circuit. the opamp Tl082 has a gain bandwidth product of 4Mhz according to the datasheet. this circuit has a bandwidth of 414.25khz. can we determine the opamp' individual gain-bandwidth product from this plot ?? if yes , how do we...

hi! can someone please help me with this problem...i have to match the open loop respone to the close loop unity feedback system of a control system. what is the relation between the two? thanx in advance

Homework Statement Find 5th roots of unity solving algebraically x^5-1=0. Using the result, find sin18 and cos18The Attempt at a Solution x^5 = 1\\ x = \sqrt[5]{1} since we have 5 roots: x_k, k = 0,1,2,3,4 \\ \\ x_k = e^{i\frac{2k\pi}{n}}, n=5 \\ x_0 = e^{i0} = 1\\ x_1 =...

i am having trouble showing that \mathbb{Q}(\sqrt{p*}) \subset \mathbb{Q}(\zeta_{p}) where p* = (-1)^{\frac{p-1}{2}}p . in other words, if p = 1 (mod 4) then p* = p and if p = 3 (mod 4) then p* = -p. i encountered this in the context of galois theory and i have no idea how to start. it seems...

I came across this term in Elements of Modern X-ray Physics by Nielsen. I'm assuming this term isn't specific to the book (because that would be ridiculous). I've always taken math courses geared toward Physics/Engineering so some math terms were never used so this is probably one of them...

In a lot of places, I can read that the roots of unity form a cyclic group, however I can find no proofs. Is the reasoning as follows: Let's work in a field of characteristic zero (I think that's necessary). Let's look at the nth roots of unity, i.e. the solutions of x^n - 1. There are n...

Hi everyone, I have a question on the discrete Fourier transform. I already know its a change of basis operator on C^N between the usual orthonormal basis and the "Fourier" basis, which are vectors consisting of powers of the N roots of unity. But if i recall correctly from complex...

Homework Statement Find the 6th complex roots of √3 + i. Homework Equations z^6=2(cos(π/6)+isin(π/6)) r^6=2, r=2^1/6 6θ=π/6+2kπ, θ=π/36+kπ/3 The Attempt at a Solution When k=0, z = 2^1/6(cos(π/36)+isin(π/36)), When k=1, z = 2^1/6(cos(13π/36)+isin(13π/36)), When k=2, z =...

Consider field extensions of the form Q(u) where Q is the field of rational numbers and u=e^{\frac{2\pi i}{n}}, the principal nth root of unity. For what values of n is the Galois group of Q(u) over Q cyclic? It seems to at least hold when n is prime or twice an odd prime, but what else...

I have become so frustrated with the Unity GUI that I my never use Ubuntu again. Not long ago, Ubuntu was the go to distro for user friendly Linux. Now it is so difficult to do even the most basic tasks and overloaded with so much useless software that I don't think I'll ever use it again...

Homework Statement Given the fact that z is one of the n-th roots of unity, find the sum below: 1 + 2z + 3z2 + ... + nzn-1Homework Equations (1-x)(1+x+...+xn-1) = 1 - xn The Attempt at a Solution honestly I don't know how to do this. any help is appreciated

"unity" means just plain regular "1"? Im not sure whether this is a physics or math question, but in many physics problems, instead of saying "1", the problem will say "unity", like "the sine of theta is unity" or the "index of refraction is unity". I am assuming "unity" means just plain...

Hey everyone! I would really appreciate some help with this problem. I have been racking my brain for hours now, and nothing seems to work/convince me. Homework Statement Show that Un \subseteq U2n for every positive integer, n. Homework Equations [1] Un = {z ε ℂ, zn = 1} [2] Un =...

1. The problem statement, all variables and given/kno(It n data I need to prove that \prod_{k=1}^{n-1}2\sin\tfrac{k\pi}{n}=n I just don't know where to start and what type of proof to do. Is there any help to get? :D Homework Equations I know this has nothing to do with an equation...

I need to factor x5 - 1.I know (x-1) is a factor and have gotten: (x-1)(x4+x3+x2+x +1) I'm not sure where to go from here. Thanks in Advance.

Homework Statement Prove that z=e^{\frac{2k\pi i}{n}},n\in\mathbb{N},k\in\mathbb{Z}, 0\leq k\leq n-1 is an n-th root of unity. The Attempt at a Solution So I know I have to come to the conclusion that z^{n}=1. I'm thinking of using the property e^{i\theta}=cos\theta+isin\theta, but...

hi, iam wondering about the unity power factor .. for example if we have a motor that will cause the power factor to be lagging by 0.3 what will happen if we add capacitor to make the power factor 1 (unity) now we will not have any reactive power and we reduced the current to the minimum...

Need help with this please: Homework Statement (1 + cosθ + isinθ) / (1 - cosθ - isinθ) = icotθ/2 The first step in the solutions shows: (2cos^2θ/2 + i2sinθ/2cosθ/2) / (2sin^2θ/2 - i2sinθ/2cosθ/2) Homework Equations I can't get there. The Attempt at a Solution I tried multiplying by: (1 -...

I'm going over some things I didn't do too well on in my latest Algebra test. One question was: List all of the roots of x^{8}\:-1\:=0, and write them in the form a+bi. So I knew I had to list all the 8th roots of unity. In other places in the test they used the notation e^{iθ} and this was a...

a,b,c are integers not all equal and w is the cube root of unity then minimum value of |a+bw+cw2|(w is not equals one). My answer |a+bw+cw2|<=|a|+|bw|+|cw2| |a|+|bw|+|cw2|=a+b+c. so at lest one value of |a+bw+cw2| will smaller than the minimum value of a+b+c. for integers this minimum...

Both my book and lecturer have in the definition a ring omitted the requirement of a unity. I was reading in my book about ideals, more specifically principal ideals. I stumbled over a formula that differed by whether or not the ring had a unity. As an example I state the two for principal left...

Homework Statement Prove that \Sigma^{n}_{k=1} wk = 0 and there has to be at least two phasors/exponentials Homework Equations complex analysis The Attempt at a Solution I tried writing out the sigma on the first line. Then I tried writing the same thing with n+1 on the...

Happy Eid to PFers who celebrate it! (I'm not sure if it's http://www.npr.org/blogs/thetwo-way/2011/08/30/140056443/when-is-eid-muslims-cant-seem-to-agree", there seems to be a bit of confusion :smile:)

Homework Statement show that cos(2pi/n) + isin(2pi/n) is a primitive root of unity Homework Equations The Attempt at a Solution if i know z = cos(2pi/n) + isin(2pi/n) is an nth root and I'm trying to prove that z is a primitive nth root. is it correct to assume that z^k is not...

Homework Statement I must show that cos(2pi/n) + isin(2pi/n) is a primitive root of unity Homework Equations a primitive root of unity is an nth root of unity that does not equal 1 when raised to the kth power for k less than n and great than or equal to 1 The Attempt at a Solution...

While attempting to solve quadratic equation application in MATHCAD (pertaining to the Markowitz Portfolio theory), I am now stumped at how to perfom what would seem to be a trivial operation, namely: setting a sum of unknown variables (i.e., a constraint) equal to '1.' For example, how can...

Show that Q/Z is isomorphic to the multiplicative group U∗ consisting of all roots of unity in C. (That is, U∗ = {z ∈ C|zn= 1 for some n ∈ Z+}.) I don't really understand how to prove this isomorphism

it is easy to construct a map from S^2 to S^2, with covering time being unity but how to do the similar task on the projected manifold RP^2=S^2/Z_2? i tried to use the stereographical trick the points on the lower half semisphere are projected onto the plane the problem is that the...

Let R be a commutative ring with unity. I and J are ideals of R. Show that If I + J = R, then I∩J=IJ. I know that IJ⊆(I∩J). But I can't do inverse.

Homework Statement z is a complex number. Find all the solutions of (z+1)^5 = z^5 The Attempt at a Solution Of course one could expand (z+1)^5, but I remeber our professor solving this with roots of unity. Can anyone help?

hi. i have recently become very interested in the idea of the nth roots of unity. i have discovered how to calculate them (using eigenvalues), and i find it very fascinating that there are not n many nth roots of unity(unlike scalars). aparently in the case where the matrix is 2x2, there are...

Homework Statement Show that, if \omega is an nth root of unity, then so are \overline{\omega} and \omega^{r} for every integer r. Homework Equations \omega=r^{1/n}e^{i((\theta+2\pi)/n)} The Attempt at a Solution I got the first part and for \omega^{r} I have it equals...

Hi all, What happens when we take the product of the imaginary parts of all the n-roots of unity (excluding 1)? I read somewhere that we get n/(2^(n-1)). How can we prove this? Thanks!

sin x. d(sin x)/dx = cos x. d(cos x)/dx = -sin x. d(-sin x)/dx = - cos x. d(-cos x)/dx = sin x. i. i^2 = -1. i^3 = -i i^4 = 1 i^5 = i. I know there is a relationship between trig, the complex numbers, and exponential functions. Is there a relationship between the pattern shown here?

Just asking: is it likely that there is any connection between roots as \sqrt[3]{1} and \sqrt[7]{1}?

I want a MATLAB code to draw the root locus for a characteristic equation of a transfer function of unity feedback, also what is the range of K that keeps the system stable , here is the characteristic equation: s^5+600s^4+50000s^3+ks^2+24ks+80k=0 please help, thanks in previous

Homework Statement I want to find out if the sixth root of unity is a subgroup of the complex numbers with multiplication. Homework Equations The Attempt at a Solution I know it's true but my problem is getting there. I know the sixth root of unity must be closed under the...

One of the question asks to find the frequency at which the gain becomes 0dB for a low pass Single Time Constant circuit. In the solution manual after finding the 3dB frequency = 10^6, it states that since the gain falls off at a rate of -20dB/dec (see attatchment for graph) starting at...

If you have a fraction, for example, \frac{1}{{1.0091532\times10^{-12}} + 1} Is there a simple way to convert it to a more easily calculated form, specifically, 1-x (where x is a very small number)

questions: why is the sum of all the roots of unity equal to zero? z^(1/n)=z1,z2,...zn z1+z2+...+zn=0 It's obviously true when there's an even number of roots, (because each root has a partner that is pi radians away and therefore the negative of the other root). but i can't figure out...

in my readings, spivak or elsewhere, I've come across this several times but i don't have the formal training (maturity) to know how to use it. intuitively: by the atlas maps on the manifold, we can chop up a manifold into patchs. for each patch, by smoothness or something, there is a smooth...

This is for 10th root unity with complex number multiplication. I am working on closure. I have multiplied 2 elements of my set and I have so far that cos[(n+k)360/10] + isin[(n+k)360/10]. Thus I know that if n+k<=9 then there is an element in the set. Now I need to show for if n+k>9 and if...

I was recently made aware of the book, "Consilience: The Unity of Knowledge". The author's name is E.O. Wilson, a well known and established biologist. http://en.wikipedia.org/wiki/Consilience:_The_Unity_of_Knowledge I saw the opportunity to bring the idea of consilience to this forum...