Numbers Definition and 1000 Threads

Solve ##Z^2\bar{Z}=8i## i am confused on how to proceed i have tried to substitute ##z=a+ib## solve the conjugate and the square, then separate the real from the imaginary and put all in a system, but becomes too complicated

Positive integers are written on all the faces of a cube, one on each. At each corner (vertex) of the cube, the product of the numbers on the faces that meet at the corner is written. The sum of the numbers written at all the corners is 2004. If $T$ denotes the sum of the numbers on all the...

Summary:: Interested in the history of the proof. Consecutive integer numbers are always relatively prime to each other. Does anyone know when this was proved? Was this known since Euclid's time or was this proved in modern times?

Summary:: Hello, my question asks if the complex exponential equation 4e^(-j) is equal to 4 ∠-180°. I tried to use polar/rectangular conversions: a+bj=c∠θ with c=(√a^2 +b^2) and θ=tan^(-1)[b/a] 4e^(-j)=4 ∠-180° c=4, 4=(√a^2 +b^2) solving for a : a=(√16-b^2) θ=tan^(-1)[b/a]= -1 b/(√16-b^2)=...

In chapter 1, page 10, real numbers are found by confining them to an interval that shrinks to "zero" length (we consider subintervals ##I_0,\,I_1,...,\,I_n##). Basically, if ##x## is between ##c## and ##c+1##, then we can divide that interval into ten subintervals, and we can, then, have...

Here is a little Science news article of a guy who got a corticobasal syndrome, which kills off brain cells. I find these kinds of weird (probably) neurologically caused mental problem very interesting. They say something about brain consciousness relationships, not clear what though...

i have to find such domain z=x+iy , y,x∈ℝ , |y-x|<=2, |x|<=2 i'm confused with |y-x|<=2, how should i proceed ? with abs of x i am ok.

Let $z_1=18+83i,\,z_2=18+39i$ and $z_3=78+99i$, where $i=\sqrt{-1}$. Let $z$ be the unique complex number with the properties that $\dfrac{z_3-z_1}{z_2-z_1}\cdot \dfrac{z-z_2}{z-z_3}$ is a real number and the imaginary part of $z$ is the greatest possible. Find the real part of $z$.

I have found code to find simply the minimum numbers needed, but I need to do it without repetition given the nature of an electric circuit. I hope that is a sufficient enough explanation of the problem. Despite being an engineering project this aspect is more mathematical.

Please help me solve this, Given digits 2,2,3,3,3,4,4,4,4, how many distinct 4 digit numbers greater than 3000 can be formed? Thank you

Let m,n be real numbers. Prove that if n>m>0 , then (m+1)/(n+1) > m/n I'm currently confuse in this one help will be very much needed

3.7.4. The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares? $x+y=16\implies y=16-x$ Then $x^2+(16-x)^2=2 x^2 - 32x + 256$ So far ... Hopefully

A recent https://mathhelpboards.com/potw-secondary-school-high-school-students-35/problem-week-411-apr-5th-2020-a-27196.html#post119308 asked about properties of a pair of positive integers $x$, $y$ such that $2x^2+x = 3y^2+y$. But it is not obvious that any such pairs exist. So the challenge...

Question is from Boas Ch. 2 Q.41 (I've the first edition) or Q 16.8 in the 3rd edition. Find the impedance of the circuit shown (R and L in series, then C in parallel with them). Circuit is essentially this (it is a closed circuit which I can't easily draw). -----R------L--- -------C---------...

Hello! :smile: I am locked in an exercise. I must find (and graph) the complex numbers that verify the equation: ##z^2=\bar z^2 ## If ##z=x+iy## then: ##(x+iy)^2=(x-iy)^2 ## and operating and simplifying, ##4.x.yi=0 ## and here I don't know how to continue... can you help me with ideas? thanks!

Is it possible two find complex numbers ##C_n##, so that both equations are satisfied \sum^{\infty}_{n=1}nC_n=0 and \sum^{\infty}_{n=1}|C_n|^2=1 ?

Proxima Centauri is 4.2 light years away. That is 24,673,274,438,400 miles. Going at the speed of the Sun through the Milky Way, 492,150 miles per hour, it would take 5,723 years to get there. In 100 years the Sun has only gone 431,123,400,000 miles, or 7 percent of 1 light year...

reducing it to various forms: for example, the one in the title, or 2*pi*k(ln m) = a(ln(n/m)), and so forth. My gut feeling is that it is true (that no such foursome exists), but manipulations have not got me anywhere. Anyone push me in the right direction? I am probably overlooking something...

Hi, I'm not sure if this is the correct forum so if I need to post elsewhere please let me know. I'm having trouble with calculating the possible combinations for six digit license plates, numbers 0-9 and letters a-z. I know the overall combinations are 1,947,792 when repetition is allowed...

Summary:: This is not a homework i just need clarification on how they got those number Any solution involving sine and cosine is my weakness when its advance or intermediate

Hello all, We know that following formulas failed to produced all prime numbers for any given whole number ##n##: ##f(n) = n^2 - n - 41##, failed for ##n = 41~(f = 1681)## ##g(n) = 2^(2^n) + 1##, failed for ##n = 5~(g = 4,294,967,297)## ##m(n) = 2^n - 1##, failed for ##n = 67~(m =...

The fundamental theorem of arithmetic applies to prime factorizations of whole numbers. Can this theorem also correctly be invoked for all rational numbers? For example, if we take the number 3.25, it can be expressed as 13/4. This can be expressed as 13/2 x 1/2. This cannot be broken...

Edit, the vector that rotates below might not rotate at all. Please forgive any mistaken statements or sloppiness on my part below. I think that by some measure a helicoid can be considered a smooth curved 2 dimensional surface except for a line of points? Consider not the helicoid above...

Suppose on day-one a number is 15 then on day-twenty the number has increased to 200. Now I want to find out what that increasing number could be on day-forty by using the exponent derived from the day- one to day-twenty increase ; x(log15) = log 200 . x = 2.301/1.176 = 1.956. So now on day...

Hi guys, I have a question relating to finding a middle number between 2 numbers as followed: You're given 2 numbers A and B and 2 other numbers X and Y The objective is to find number C so that A+/- x=C And B +/- y = C (condition is B<C<A or C is always between A and B) The rule for x and y...

Recently I created a spreadsheet that generates Phythagorean triples. Curious, instead of using only positive integers for the values of m and n, I found that as long as m>n, the sides 2mn, msq + nsq, msq - nsq, still form the sides of a right triangle even though m and n are non-whole...

I understand that the Dual Space is composed of elements that linearly map the elements of the Vector Space onto Real numbers If my preamble shows that I have understood correctly the basic premise, I have one or two questions that I am trying to work through. So: 1: Is there a one to one...

The sum of ten integers is 0. Show that the sum of the fifth powers of these numbers is divisible by 5. For this one I don't know what I have to do at all other than brute-forcing which may even be impossible.

I have some questions about this video. I have watched other videos in this series. Otherwise very nice series, but I think there may be mistake. Isn't the video flawed because it forgot forgot 0'th component of 4-fector ##A## aka ##\varphi## in 3-vector representation, I think it because...

I know this topic was raised many times at numerous forums and I read some of these discussions. However, I did not manage to find an answer for the following principal question. I gather one deals with the same set in both cases equipped it with two different structures (it is obvious if one...

i have not clue if this is the right place to ask if i had 2 numbers and i wanted to blend between them but instead of a linear way it was in an inverse square way.. how would that math go? so if i had A=1 and B=9 and wanted the number at 0.5 it would be 4.. or if i wanted the number at 0.85 it...

Hi everyone. I haven't been here in years, I'm surprised the account still works. Anyway. I have a mathematic thought/question that I really want to learn about. I realize this isn't going to be the easiest thing to explain if it is even possible, so please forgive me. So, What I want to do...

are there any whole numbers for x,y,a,b, that satisfy x^3-y^2+ab=a-b(x+y)

I've got the problem well. The sum of the given numbers is 2n(2n+1)/2 = n(2n+1). And there are n buckets, so the average sum of numbers of each bucket is 2n+1.I've come to this so far. But I'm not sure whether the numbers are to be distributed over all 'n' buckets or some of the buckets can...

Solution to the problem tells us that ##S_5 + i S_6## is the sum of the terms of a geometric sequence and thus the solutions should be : $$S_5 = \frac{\sin( (n+1) x)}{\cos^n(x) \sin(x)},\,\,\,\, S_6 = \frac{\cos^{n+1}(x) - \cos((n+1)x)}{\cos^n(x) \sin(x)} , x \notin \frac{\pi}{2} \mathbb{Z}$$...

i can get to 3i+1/1-3i but no further. I take it this is the correct way to start

All i was able to think was that i have to find a point (x,y) such that sum of its distances from points (0,0),(1,0),(0,1) and (3,4) is minimum.I tried by assuming the point to be centre of circle passing through any of the above 3 points,But it didn't helped me.

I came across a significant figures problem today that I need information on. The problem is this: "What volume of water can a cylindrical container hold of it is 13.0 cm tall and 12.0 cm in diameter? Show your work and express the answer in scientific notation using significant figures." Of...

Paul Dirac proposed a hypothesis called "Large Numbers Hypothesis" (https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis), where he basically stated that, if he was correct, laws of physics would change with time. But what about fundamental laws and constants? (Not only 'effective'...

##cos(\omega)## is $$\frac{e^{j \omega } + e^{-j \omega }}{2}$$ ##sin(\omega)## is $$\frac{e^{j \omega } - e^{-j \omega }}{2 j}$$ I also know that ##cos(\omega - \pi / 2) = sin(\omega)##. I've been trying to show this using exponentials, but I can't seem to manipulate one form into the...

Summary: Trouble with infinity and complex numbers, just curious. I'm not too familiar with set theory ... but <-∞, ∞> contains just real numbers? Does something similar to <-∞, ∞> exist in Complex numbers? My question, is it "wrong"?

Gödel numbers are used to encode wffs of formal systems that are strong enough in order to deal with Arithmetic. In my question, Gödel numbers are used to encode wffs as follows: Syntactically (by formalism without semantics) there is set A (the set which is postulated to be infinite), such...

Summary: Which properties of ##\mathbb{C}## are actually necessary? The following is speculative as well as a honestly meant question about the way QM is modeled. I don't want to create a new theory, just understand the necessities of the old one. Physicists use complex numbers for QM. But...

--Continued-- 7) Let ##\sum_{k=0}^9 x^k = 0## Find smallest positive argument. Same thing as previous question, but I guess I can expand to ##z+z_{2}+z_{3}+...+z_{9}=0## ##z=re^{iθ}## ##re^{iθ}+re^{2iθ}+re^{3iθ}+...## What do I do to proceed on? Cheers

Hello all! Thanks for helping me out so far :) Really appreciate it. I don't seem to understand some of the questions presented to me, so if anyone has an idea on how to start the questions, please do render your assistance :) 4) Take ##3+7i## is a solution of ##3x^2+Ax+B=0## Since ##3+7i## is...

Hello, here with some complex number questions which I need some assistance in checking :) 1) z=3+5i1+3iz=3+5i1+3i Find Re(z) and Im(z) My answer is 9595 and −25−25 respectively. Checked by Wolfram 2) Find principal argument of the complex numberz=−5+3iz=−5+3i and express it in radians up to 2...

Hello everybody! I have a problem with this exercise when I have to find the possible angular momentum. Since ##\rho^0 \rho^0## are two identical bosons, their wave function must be symmetric under exchange. $$(exchange)\psi_{\rho\rho} = (exchange) \psi_{space} \psi_{isospin} \psi_{spin} =...

The book uses ladder operators ##L_+## and ##L_-## to find the eigenvalues ##m## of ##L_z##. By first deducing that these operators raise or lower the eigenvalue by ##\hbar##, and then deducing that the lowest eigenvalue is the negative of the highest eigenvalue ##l##, it proves that ##m = -l...

I'm kind of stuck over here at one part, but something is telling me that it might be wrong too :( Do assist, thanks.