Numbers Definition and 1000 Threads

The unit right now is electrostatics, but this question is really just vectors, nothing to do with charges or anything... anyways here is the info: 1. Homework Statement Three identical point charges, A, B, and C are located as shown here: The force A-on-C is the same as the force B-on-C...

I work a lot in binary. I am organizing some of my work and need a way to write expressions. I can always create my own notation, but i would rather not invent something that already exists. 1011 is binary for 11 base 10. I use this {3,1,0} to represent the binary with just exponents. When I...

1. Give a formula for the values on m such that z^m=z z=cos(7pi/6)+i*sin(7pi/6) 2. If i use de movires i get 3. m*7pi/6=7pi/6 + k*2pi But then i get the value that k=12/7, Which is the wrong formula. The correct answer is 1+12k for k=0,1,2...

Homework Statement Let ##z_1,z_2,z_3## be three complex numbers that lie on the unit circle in the complex plane, and ##z_1+z_2+z_3=0##. Show that the numbers are located at the vertices of an equilateral triangle. Homework EquationsThe Attempt at a Solution As far as I understand, I need to...

Prove that $8^{91}\gt 7^{92}$.

so(4) is the symmetry algebra of Keplerian motion. Its structure is well known. The principal quantum number n must be a positive integer. The associated Casimir operator has eingenvalues n^2 - 1 . The secondary quantum number j is integer and can take any value from zero to n-1. The...

Dear Physics Forum friends, what are some good books for learning the p-adic numbers? What are the necessary pre-requisites? Do I need to know introductory number theory or basics of algebraic/analytic number theory?

Homework Statement Reflection of the line ##\bar{a}z + a\bar{z} = 0## in the real axis is Homework EquationsThe Attempt at a Solution I know that a line in the complex plane is represented as ##\bar{a}z + a\bar{z} + b= 0## and that its slope ##μ = \dfrac{-a}{\bar{a}}##. I'm not sure how to do...

Find all positive integers whose square end with 444.

Or basically anything that isn't a positive integer. So I can prove quite easily by induction that for any integer n>0, De Moivre's Theorem (below) holds. If ##\DeclareMathOperator\cis{cis} z = r\cis\theta, z^n= r^n\cis(n\theta)## My proof below: However I struggle to do this with...

With the quantum numbers l=1, n=2 and m=-1 how do I calculate the total energy E, L2 (the square of the orbital momentum) and Lz (the z-component of the orbital angular momentum. I've been trying for two hours and am getting no were. Please help

Homework Statement This problem is from MIT OpenCourseWare- a diagram is attached to clarify certain definitions. I'd like to check my answers. The degree sequence of a simple graph is the weakly decreasing sequence of degrees of its vertices. For example, the degree sequence for the 5-vertex...

Let's say we have two numbers represented as a "tower" of exponentials, a^b^c^d and w^x^y^z (powers calculated right to left) and we want to compare them, not necessarily calculating their values. Their values are so huge, they can't be represented on a computer or calculator. Is it possible to...

I am not certain this is the best place to post this, but not sure General Physics would have been appropriate either. Feel free to move this. I am writing a paper for a quantum physics class, and the professor wants the paper to be in the APS (Physical Review) style. I looked through their...

This may be a simple thing but due to some reason I am not able to understand. I am not able to understand an example from Brown-Churchill book. I have provided the screenshot in the attached picture. Request help.

Homework Statement I am not able to understand an example from Brown-Churchill book. I have provided the screenshot in the attached picture. Request help. Homework Equations No The Attempt at a Solution No

Homework Statement Show that the set ##\{x \in \mathbf Q; x^2< 2 \}## has no least upper bound in ##\mathbf Q##; using that if ##r## were one then ##r^2=2##. Do this assuming that the real field haven't been constructed. Homework Equations N/A The Attempt at a Solution Attempt at proof: ##r\in...

Homework Statement a) The complex number ## 1-i ## is denoted by ##u##. On an argand diagram, sketch the loci representing the complex numbers ## z## satisfying the equations ## |z-u|= |z| and |z-i|=2 ## b) Find the argument of the complex numbers represented by the points of intersection of...

Solve the equation np_n+(n+1)p_{n+1}+(n+2)p_{n+2}=p^2_{n+2} where n\in \mathbb N^* and p_n , p_{n+1} , p_{n+2} are three consecutive prime numbers. ------------------------------------- A solution is n=2,p_2=3,p_3=5,p_4=7. May be other solutions?

Homework Statement Predict the number of unpaired electrons [Cr(H2O)6]3+ Homework EquationsThe Attempt at a Solution I under stand how to fill out the MO with the eg and t2g and all but I'm confused about determining the number of electrons. The answers state this is an octahedral d3 but I...

Hi! We have discussed complex numbers in class and their conjugates. From what I understand only the imaginary unit is conjugated. But I wonder if there are such things as real conjugates of complex numbers? Given the following points: $$A=(-2+i)$$ $$B=(2+3i)$$ $$C=(-4-3i)$$ $$D=(-4+i)$$ I...

Hi, I'm a little unsure how to input large numbers into the TI-83 calculator using invNorm and normalcdf. Here's the question to the problem: A study of VCR owners found that their annual household incomes are normally distributed with a mean \$41,182 and a standard deviation of \$19,990...

Find all the natural numbers $a$ and $b$ such that $(a^2+1)(b^2+1)+45=2(2a+1)(3b+1)$.

Homework Statement The complex number ##u## is defined by ## u= 6-3i/1+2i## i) Showing all your working find the modulus of u and show that the argument is ## -1/2π## ii) For the complex number Z satisfying ##arg(Z-u)= 1/4π##, find the least possible value of mod | Z | iii) For complex number...

I found this article fascinating. Imagine overlooking something so simple for so long!

Take a number r that is n-digits long where n is finite. so if r =2385813... $$r_1r_2r_3...r_n$$ $$r_1 = 2$$ $$r_2 = 3$$ $$r_3 = 8$$ etc.. I postulate (since I don't know this is true): Every such number can be expressed as a division between two other numbers, say a and b. $$r = \frac{a}{b}$$...

For any $a \in \mathbb{R}$, let $a^3$ denote $a \cdot a \cdot a$. Let $x, y \in \mathbb{R}$. 1. Prove that if $x < y$ then $x^3 < y^3$. 2. Prove that there are $c, d \in \mathbb{R}$ such that $c^3 < x < d^3$.

I'm finding it difficult to find the exact value of epsilon on python? Moreover, I am also supposed to find the smallest floating point number as well. Wikipedia tells me that the machine epsilon is 2−52 ≈ 2.22e-16 for 64-bit IEEE 754 - 2008? Is this the exact value on Python? Outside of...

Homework Statement The BCH formula states that the product of two exponentials of non commuting operators can be combined into a single exponential involving commutators of these operators. One may write that ##\ln(e^A e^B) = \sum_{n \geq 1} c_n(A,B)## where $$c_{n+1} = \frac{1}{n+1} \left(...

Hello guys I am trying to write a code which is below; But my results seems to be fairly wrong. I noticed some of my real numbers are not what I assigned them. For example Ks shows on the watch window as 9.9999999E-5. How can I fix such situation? program hw1 REAL:: G,DVIS,Ks...

Hi All, Just curious: what kind of data types does one usually use for web addresses, for phone numbers? EDIT: I am using MSSQL 2014 . Thanks.

Dear All I just have a question. We say that the SU(2) doublet have the same value of isospin but the particles of this multiplet differs by I3. Now what quantum number the particles of SU(3) multiplet share. Thank you

Find the solutions in natural numbers for the following equation: \frac{10}{x+10}+\frac{10\cdot 9}{(x+10)(x+9)}+\cdots+\frac{10\cdot 9\cdot 8 \cdots\cdot 3 \cdot 2 \cdot 1}{(x+10)(x+9)(x+8)\cdots(x+3)(x+2)(x+1)}=5

Determine, without the help of calculator, which of the following is bigger: 1016^{11}\cdot 3016^{31} versus 2016^{42}

Homework Statement Write a program that will print all highly prime numbers from the input interval <a,b>. Prime number is highly prime if deletion of every digit from right is a prime. Example: 239 is highly prime because 239,23,2 are primes. 2. The attempt at a solution Could someone point...

Well, let's look at how this works. Quadratic equations can have either 1, 2, or no zeroes. If it has no real zeroes, the zeroes it DOES have are complex, so that's obviously not it. Let's imagine ax^2 + bx + c = 0 has one zero, call it \alpha (Cuz it looks pretty). Then that means ax^2 +...

I want to convert a recursive real formula to rational number representation, but I get the wrong response. For the real formula: k = 1.9903694533443939 u1 = -12.485780609032208 u2 = -6.273096981091879 u3 = k * u2 -u1 /// 1st iteration u3 = -1.7763568394002505E-15 // approx. zero /// 2nd...

So I have an interest in hypercomplex numbers and Clifford Algebras and was wondering a few months ago about other hypercomplex numbers besides the celebrated Quaternions and Octonions. I tried to construct a 5D complex number system using a Cayley table but noticed that entries in rows and...

Write a while loop that prints 1 to userNum, using the variable i. Follow each number (even the last one) by a space. Assume userNum is positive. Ex: userNum = 4 prints: 1 2 3 4 #include <iostream> using namespace std; int main() { int userNum = 0; int i = 0; userNum = 4; //...

Call a nonempty (finite or infinite) set $A\subseteq\Bbb R$ complete if for all $a,b\in\Bbb R$ such that $a+b\in A$ it is also the case that $ab\in A$. Find all complete sets.

Homework Statement Question 3.b. - http://imgur.com/ztLiRvx Homework Equations For the sake of simplicity, let's assume that lambda = x. The Attempt at a Solution I tried equating the real an imaginary parts of arctan(1/4). Real: x/2 + 3 = 4. This gives x = 2. Imaginary: x/2 - 3 = 1. This...

Dear Sir, Assuming that my lottery machine can generate 10 numbers (0..9), in which 0 and 9 are supposed to be starting and ending states of my Markov chain. I apply Markov chain to model each number appearance because I would want to modify the random generation process into, say, my own...

We increase by 1 each of three prime numbers, not necessarily distinct. Then we form the product of these three sums. How many numbers between 1999 to 2021 can appear as such a product?

Reflecting about that i.e. just 6 parameters whose value have to be like they are with a high degree of precision to have a universe like ours and that the probability for having those 6 values to be as they are should have a very low probability in connection with the theories about multiverse...

I was just wondering when you type some numbers into your computers calculator or into a website, how does it find the answer? Obviously for very small numbers like 4x12 it could do this just by addition. What about for massive calculations? For example 102! I typed this into Wolfram Alpha and...

Hello, I was given a question (not a HW question..) in which i was asked to calculate the number of ways to sort n numbers into k groups, where for any two groups, the elements of one group are all smaller or larger than the elements of the other group. The answer is supposed to be...

what is meaning of this ? 132kV Transformer INCOMER CTs (900-600-300/1-1-1-1-1A) NUMBER OF CORES - 5 is it single CTs package or different CTs ?

Homework Statement Express the following using existential and universal quantifiers restricted to the sets of Real numbers and natural numbers Homework EquationsThe Attempt at a Solution I believe the existence of rational numbers can be stated as: ##(\forall n \in \Re)(\exists p,q \in...

Homework Statement [/B] Z=((2z1)+(4z2))/(z1)(z2) where Z1=4e^2pi/3 Z2=2/60 degre, z3=1+i The answer must be in polar form r/theta Homework Equations Well in the upper section The Attempt at a Solution After do some operations i get to this and unable to convert to polar form... -...

Homework Statement Find the sum of the numbers between 200 and 800 inclusive, which are multiples of 6, but not multiples of 9. Homework EquationsThe Attempt at a Solution Numbers that are multiples of 6 should be: a = 6n, n ∈ ℤ and a is any multiple of six. 200 = 6n → n1 = ##\frac{200}{6}## =...