Numbers Definition and 1000 Threads

Homework Statement well this is not exactly a homework, i had an argument whith my teacher about my grade in a test, because i put a complex number in the form of R,theta and she claims that the form was costheta+isentheta, and i know that but i need to prove in a book that...

Is the fact that QM uses complex numbers should be considered as a math artefact (as it is the case when complex numbers are used for alternate current circuit analysis), or, alternatively, it has some deep and important relation to the nature (or at least to the nature of the quantum theory)...

Prove, that the sequence: $a_n = \left\lfloor{2^n\sqrt{2}}\right\rfloor,\;\;\;\;n = 1,2,3,..$- contains infinitely many composite numbers.

Ive tried to make each variable relate to a but it hasn't worked.

Can we order Complex Numbers ? I searched a bit most places says it can but not like the real numbers. I am confused a bit.And I am not sure abouth the truth of those sources. Thanks

Homework Statement http://prntscr.com/eqhh2p http://prntscr.com/eqhhcg Homework EquationsThe Attempt at a Solution I don't even know what these are, it is not outlined in my textbook. I'm assuming I am is image? But how do you calculate image even? As far as I'm concerned I am has to do wtih...

I'm having trouble finding the correct names for the 4 standard labels: n, l, m, s. Where might I find, free online: their correct names (ie, no colloquialisms or short cuts) and the accepted formula for each (to be sure I use them correctly)? Thanks.

I have a question stating to derive the functions x |-> f_1(x)=x^3 and f_2(x)=thirdrootof(x) on their domains of definition based on the asymptotic relative condition number KR = KR(f,x). I'm not sure where to start with this question, I'm not sure if I even understand it. Do I find the...

Hi, I am trying to solve this series generally: the series: 3 7 12 18 25. i tried using x(n) = 3 + 4n. But this doesn't work.. Please help.

if ## a,b,c,d,e ## are positive real numbers, minimum value of (a+b+c+d+e)( \frac{1}{a} +\frac{1}{b} +\frac{1}{c} +\frac{1}{d} +\frac{1}{e} ) (A) 25 (B) 5 (C) 125 (D) cannot be determined My approach : expanding the expression , i get 5+a( \frac{1}{b} +\frac{1}{c} +\frac{1}{d} +\frac{1}{e}...

Mod note: added code tags using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace ConsoleApplication1 { class Program { static void Main(string[] args) { List<int> number = new List<int>(1000); // int list for 1000 numbers...

In this Khan Academy video they say that it is ok to break the square root ##\sqrt{a\cdot b}##, with ##a, b \in \mathbb{R}##, into the product of two square roots ##\sqrt{a}\cdot \sqrt{b}##, only when: (1) both are non negative, (2) one of the two is negative and the other is possitive. I...

I was trying to find the compressibility of water and compressibility of air to compare. For compressibility of water I found 46.4e-6 For compressibility of a gas... I am having a tough time finding anything. compressibility factor I can find, which is 1 for Hydrogen... but how does that relate...

Homework Statement Is the group of positive rational numbers under multiplication a cyclic group. Homework EquationsThe Attempt at a Solution So a group is cyclic if and only if there exists a element in G that generates all of the elements in G. So the set of positive rational numbers would...

I'm getting pretty discouraged because I'm a straight A engineering student, but this semester I'm getting bad grades because I'm plugging things into my calculator wrong. I study a ton, and I definitely know the material, I just plug things into my calculator wrong and get the wrong answer. In...

$x,y\in N$ $\dfrac {1}{x}+\dfrac {1}{y}=\dfrac {1}{2010}---(1)$ How many pairs of $(x,y)$ we may get to satisfy (1)

z is either a real, imaginary or complex number, and z^12=1 and z^20 also equals 1. What are all possible values of z? I know 1 and -1 are them, and I think its also i and -i?

What am I doing wrong here? The prompt is https://www.hackerrank.com/challenges/kaprekar-numbers and my well-commented solution is using System; using System.Collections.Generic; using System.IO; using System.Linq; class Solution { // Returns the number represented by the digits in the...

Homework Statement So in C an integer is stored as a 32 byte value. Were the 32nd byte is the byte that determines if the value is negative or positive. I created a loop were I set the integer i equal to 1. Each time I cycle through the loop I left shift the variable i by one. Meaning that...

Homework Statement "If no prime number ##p## divides a hypothetical solution ##(x,y,z)∈ℕ×ℕ×ℕ## to the equation ##x^3+y^3=z^3##, prove that exactly one of x, y and z is even." Homework Equations Given: ~##∃p:(\frac{x}{p},\frac{y}{p},\frac{z}{p})∈ℕ×ℕ×ℕ## such that ##x^3+y^3=z^3##. In other...

I have authored documents of 40 years of computer software development with a mind to collect them into a publication at some point. They have been built around several software topics but mathemetics is a favorite of mine. I find a point of inspiration and write a piece of software around it...

There a simple math example that I am confused ##(\sqrt {-4})^2## Theres two ways to think 1-##\sqrt {-4}=2i## so ##(2i)^2=4i^2## which its ##-4## 2-##\sqrt {-4}##.##\sqrt {-4}##=##\sqrt {-4.-4}=\sqrt{16} =4## I think second one is wrong but I couldn't prove how, but I think its cause ##\sqrt...

We talked about Fibonacci numbers, and I wondered: Can any natural number be construed by a sum of unique Fibonacci numbers? My guess was yes, and a C program I wrote confirms that to be up to about 2,000, but that's of course is no proof. The best semi-proof I could come up with is that the...

Homework Statement If $$C = 1+cos\theta+...+cos(n-1)\theta,$$ $$S = sin\theta+...+sin(n-1)\theta,$$prove that $$C=\frac{sin\frac{n\theta}{2}}{sin\frac{\theta}{2}} cos\frac{(n-1)\theta}{2} \enspace and \enspace S = \frac{sin\frac{n\theta}{2}}{sin\frac{\theta}{2}}sin\frac{(n-1)\theta}{2}$$...

Hi. Trying to solve the Gibbs paradox for two identical volumes of ideal gas with ##N## particles each, I found the mixing entropy to be $$\Delta S=2N \log(2)-\log((2N)!)+2\log(N!)\enspace .$$ The usual approach now uses Stirling's approximation to the order ##\log (n!)\approx n\log (n)-n##...

Homework Statement If Z1+Z2+Z3=0 and Z1*Z2 + Z2*Z3 + Z3*Z1=0 and Z1, Z2, Z3 are all complex, what is the value of (|z1|+|z2|+|z3|)/(|z1*z2|+|z2*z3|+|z3*z1|) Homework EquationsThe Attempt at a Solution I tried to multiply the equations by the product of all conjugates and reach some...

Find x and y if x, y are members of real numbers and: (x+i)(3-iy)=1+13i I first expanded it to give: 3x-yix+3i+y=1+13i Then I equaled 3x+y=1 and -yx+3=13 But afterwards I do other steps and get the wrong answer.

Homework Statement So we have been doing complex numbers for about 2 weeks and there is this one equation I just can't solve. It's about showing the set of solutions in graphical form (on "coordinate" system with the imaginary and the real axis). So here is the equation: Homework Equations...

I have to find a primitive function below using the Euler formulas for ##\sin x## and ## \cos x## The problem $$ \int e^{2x} \sin 3x \ dx $$ Relevant equations ## \cos x = \frac{e^{ix}+e^{-ix}}{2} \\ \sin x = \frac{e^{ix}-e^{-ix}}{2i} \\ \\ \int e^{ix} \ dx = \frac{e^{ix}}{i} ## The attempt...

Most than a question, I'd like to show you what I've got to understand and I want you to tell me what do you think about it. I'm not a math expert, I just beginning to study maths, and I'm reading Elements by Euclids, and I've been doing some research on immeasurable numbers. My statement is...

Is there a shortcut method to find 7373×5353 if we know 73×53, or any general formula for this type of questions

What is the probability of having these 2 sets of numbers with 4 digits the same and 1 unique digit? Thank you. 12,547 11,425

Hello friends from afar. I ran into what I felt to be somewhat of an odd question: Prove that some odd numbers are primitive roots modulo pm for each odd prime p and each positive integer m. It feels dodgy given that any odd number n = p1p2 ⋅⋅⋅ ps cannot be a primitive root of a prime number...

I don't see why imaginary numbers were necessarily so difficult among top mathematicians back then. From pleano's axioms, we can derive the fact that any negative natural number times another negative natural number must be positive. Then this result extends to the reals, using theorems derived...

Hello! This is my first post on these forums. So I was stuck with this question in my Mathematical Analysis exam, and it is as follows: ƒ(x) = 0 if x ∉ ℚ and (p + π) / (q + π) - (p / q) if x = (p / q) ∈ ℚ (reduced form). 1- Prove ƒ is discontinuous at all rational numbers except 1: This is...

Homework Statement I am having trouble solving systems of equations when they contain complex numbers. The context is circuit theory and phasors. For example, I am given this And the goal is to find I2 and Voc, which you can see the answers for. I just don't know how to manipulate the numbers...

I was taught a scalar is a quantity that consists of a number (positive or negative) and it might include a measuring unit, e.g. 6, 5 kg, -900 J, etc. I was wondering if complex numbers like 3 + 7j (where j is the square root of minus 1) can be considered scalar quantities too, or is it that...

Homework Statement Sketch the loci, find centre point and the radius of the circle. args((z-3i)/((z+4))=π/6[/B] Homework Equations args(x/y)=args(x)-args(y) Circle theorem - inclined angle theoremThe Attempt at a Solution I sketched the circle with major arc. Radius= using Pythagorus I got...

Homework Statement Prove that each subfield of the field of complex numbers contains every rational number. ' From Hoffman and Kunze's Linear Algebra Chapter 1 Section 2 Homework EquationsThe Attempt at a Solution Suppose there was a subfield of the complex numbers that did not contain every...

Homework Statement Prove: If p is prime and m, n are positive integers such that p divides mn, then either p divides n or p divides m. Is anyone willing to look through this proof and give me comments on the following: a) my reasoning within the strategy I chose (validity, any constraints or...

uhh, how would we get a better way?

Here is a problem I am working on: Using the Rule of Sarrus: $$\begin{vmatrix} x & y & z \\ z & x & y \\ y & z & x \\ \end{vmatrix} =x^3+y^3+z^3-3xyz,$$ find $x, y, z$ such that $x^3+y^3+z^3-3xyz = 315.$ And here is what I have gotten so far: By row and column operations and by factoring out...

Determine all three real numbers $a, \,b$ and $c$ which satisfies the conditions $a^2+ b^2+ c^2= 26$, $a + b = 5$ and $b + c\ge 7.$

Hi PF! I have a .txt file with spaces and letters, along with numbers. It looks something like this: 12.0 42.0 21.0 32.0 ICF-8-1 23.0 24.0 46.0 600.0 Additionally, the first two sets of numbers each represent a coordinate pair. Then the first coordinate is (12,42) and the second is...

I'm having trouble figuring out to get the answers from the 2 equations. The phasors and complex numbers confuse me. Do I need to change the phasor form? How do I go about doing this thanks! (Not homework question I am trying to figure this for my exam!)

Why √[(-a).(-b)] can't be written as √(-a).√(-b) Is it only because complex number do not work for this statement. Just like here: √ab = √[(-a).(-b)] = √a√bi^2 = -√ab which is wrong. We can separate √(-4)(9) = √-36 = 6i , √4i.√9 =6i, but why can't we separate for two negative numbers inside...

I have been reading about Landau levels for a two-dimensional system of charged particles in a perpendicular magnetic field and I have trouble understanding why there is degeneracy in the system. Let me provide some background to my problem. In the presence of a magnetic field, the momentum of a...

What does the N^2 mean in this case? (Image below) Does it mean, for all two pairs of natural numbers, a and b? How would I represent non pair numbers, i.e. how would I write "For integers k,l, and m such that k>1, l>2, m>k+l" all in one line?

I am attempting to find the numbers above the average number of a set of numbers in an array. I am having trouble understanding why my output for the list of numbers above the average is so...weird. I'd appreciate the help! My code: public class Inequality { public static void main(String[]...

Show that there exists 2016 consecutive numbers that contains exactly 100 primes.