Numbers Definition and 1000 Threads

Why do we represent waves as complex numbers? Why won't real suffice? Thanks for any help.

Homework Statement 1) Apparently it's a true statement that the quantum numbers 2, 0, 0, 1/2 can apply to any of Cl's electrons. But chlorine's electron configuration is [Ne]3s^2 3p^5. What happened to the n = 3 electrons? 2) How many valence electrons can a ground state oxygen atom have...

A) I understand that complex numbers come in the form z= a+ib where a and b are real numbers. In the special case that b = 0 you get pure real numbers which are a subset of complex numbers. I read that both real and imaginary numbers are complex numbers so I am a little confused with notations...

Homework Statement I am to consider the Zeeman Effect. I need to calculate the energy level shifts for a given magnetic field corresponding to different quantum numbers. I'm having a hard time knowing when a quantum number Q should be interpreted as just Q or as (Q, Q-1, ..., 0, ..., -Q)...

Convert the following numbers to their floating point binary equivalent. Can someone check my work? a) 18.25 so I got 10010.01 I couldn't find an online conversion calculator anywhere. can you also check my answer for this one? b) 1027.375 I got 10000000011.010

1111010 x 1001 is a negative * a negative so I should get a positive right? which I got 0001001010. BUT, if it's -122 x -9 = 1098. How come I get a positive number that doesn't equal 1098. Aren't you supposed to disregard the most left bit if it's more numbers than your original like wouldn't...

[Mentor's note: This post does not use the template because it was originally posted in a non-homework forum. I moved it here instead of deleting it and asking the poster to re-post, because he has already shown a reasonable amount of effort.] I am having a bit of trouble with this homework...

Perform the following operations involving eight-bit 2's complement numbers and indicate whether arithmetic overflow occurs. 1) 01110101 + 11011110. So I have a +Positive + a -Negative number. So I just added normally, and got the result of 01010011. I realized before I started the problem I...

Homework Statement A Solid rod with .375 in. D sits glued in the hole with .38 in. D. There is glue only on the annulus of the rod. A force is applied to the back side of the rod until the glue bond is fully sheared and the rod falls out. Find the shear stress Homework Equations...

From numbers 1 to 10 find the probability the number chosen is even number or a multiply of 3 Here in this question what mean by (multiply of 3)

I don't understand something. Perform the following operations involving eight-bit 2's complement numbers and indicate whether arithmetic overflow occurs. If I have 01110101 +11011110 I know that the second term is negative because there is a 1 in front. Now, because it is negative do...

Perform the following operations involving eight bit 2's complement numbers and indicate whether arithmetic overflow occurs. 1. 00110110 + 01000101 = 01111011 Overflow: there is none because we are adding to positive numbers. Did I do this correctly?

Homework Statement Show that (1+i) is a root of the equation z4=-4 and find the other roots in the form a+bi where (a) and (b) are real.Homework Equations Using De Moivre's Theorem zn=[rn,nθ] Modulus(absolute value of z) = 4 Argument = ? The Attempt at a Solution r4=4 → r = (4)^(1/5)...

Hi MHB, This problem has given me a very hard time because I have exhausted all the methods that I know to figure out a way to find for the values for both a and b but no, there must be a trick to this problem and I admit that it is a question that is out of my reach... Could you show me...

Hi there, As my Maths skills suck, I'm not entirely sure if I've worked out the following correctly: Using the combinations calculator - http://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html - the total amount of possible numbers drawn in a game (80), and how...

Convert the decimal numbers 73, 1906, -95, and -1630 into signed 12 bit numbers in the following representations: a) Sign and magnitude b) 1's complement c) 2's complement So 73 is easy. It's positive so I know it starts with 0. so I know that 73: sign and mag = 000001001001, 1s complement =...

Determine the decimal values of the following 1's complement numbers: So i understand that if the left most bit number is a 1 it is a negative, and if it is a 0 it is poisitive. But my question is why do they start out with -511 when 2^9 is obviously -512. Why are they adding 1 to it initially...

Determine the decimal value of the following unsigned number. So here was the first one I did. Which is easy. I completely understand this one. (3751)8 = 2025 I know this because: 1 + 5 * 8^1 + 7 * 8^2 + 3 * 8^3 = 2025. But then they gave me this one. b) (A25F)16. <-- They want me to...

Homework Statement Let a and b be real numbers with a < b. a. Derive a formula for the distance from a to b. Hint: Use 3 cases and a visual argument on the number line. b. Use your work in part (a) to derive a formula for the distance between (a,c) and (b,c) in a plane. c. Use the...

Greetings , Im taking an online course on mathematical thinking, and this question has me stumped. r is irrational: Show that r+3 is irrational Show that 5r is irrational Show that the square root of r is irrational. Im sorry if i posted this in the wrong forum, but I am not sure...

Homework Statement (a) Find the remainder when 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divided by 5. (b) Generalize this resultHomework Equations Congruence Modulo a\equivb mod n also a=n*q+b where q is some integer.The Attempt at a Solution The remainder for 1^99 would be 1. The remainder for...

Hello, I am embarking to read Spivak's book on Calculus, and have come across some difficulty with something that is perhaps rather trivial. In the third edition, there is a section entitled Basic Properties of Numbers. Near the end of page 7, the author begins discussing how he will use...

Hello I have 5.8 moles of KOH. 1Mole of KOH= 56.11g So: 5.8moles of KOH x 56.11g/1mole= 325.438g of KOH If, I want to follow the significant figures rules, what is the answer? Is it 330g? If yes, it seems inaccurate.

It is known that prime numbers become sparser and sparser, with the average distance between one prime number and the next increasing as n approaches infinity. Dividing an even number by 2 results in a bottom half from 1 to n / 2 and a top half from n / 2 to n. For a particular sufficiently...

I am asked to come up with two 4-bit binary numbers, that when subtracted, provide the wrong result for both the unsigned and signed cases, inspecting only the first 4 bits of the output. I have come up with numerous combination where the unsigned is correct, the signed is wrong, and vice...

Resident number theorist and global moderator at MMF (Charles R Greathouse IV) has graciously given me permission to reproduce an image he created to demonstrate the different classes of numbers: Rings are depicted in a ring, fields in an octagon, and algebraically closed fields in a...

Homework Statement Prove for complex number z1, z2, ..., zn that: \mathbb{R}e\left \{ \sum_{k=1}^{N} z_{k}\right \} = \sum_{k=1}^{N}\mathbb{R}e\left \{ z_{k} \right \} Homework EquationsThe Attempt at a Solution Not sure how to setup this problem. I was thinking: \mathbb{R}e\left \{...

Let $a, b, c, d$ be real numbers such that a=\sqrt{4-\sqrt{5-a}}, b=\sqrt{4+\sqrt{5-b}}, c=\sqrt{4-\sqrt{5+c}} and d=\sqrt{4+\sqrt{5+d}}. Calculate $abcd$.

So, I'm not 100% sure if this is actually in the correct forum or whether it should be under Mathematics. Anyway, our lecturer told us that we'd soon cover "Floating Point Numbers". Could someone give me a basic, somewhat simple explanation of what these are? Possibly with a few examples. Just...

Hi, A bit is a fundamental unit of information, classically represented as a 0 or 1 in your digital computer. I now number 100 is written in classical bits 0 and 1 as 1100100.Then How to represent 100 in qbits. cheers!

what is the defination of complex no?

Homework Statement This is not a homework question, but I'm facing this from my research. I have N complex numbers defined as x_{n}=|\alpha_n| \cdot e^{j \theta_n} for n = 1,\ldots,N and my observation is the sum of those numbers r = \sum_{n=1}^{N} x_n . From the observation r, I...

Lets say z!=0, and zeC(is complex). So for example is z=2+3i. z^0=1 => (2+3i)^0=1. I am correct? I know that all numbers in zero make us one,but it works with complex numbers too?

I know that in logarithms we can not set as base a negative number,but look at this(in the brackets I will put the base.): log(-2)-8=3 Mathematics say that is wrong,but why? If we tell -2^3=-8 we have a correct result. So? Thank you!

Complex numbers? Since the system is not an ordered pair, how then is it defined using the complex system as an ordered system to plot the z axis (Plane) to use a function? At the point we input each point of the Real and imaginary plane into a function to get out an answer in the Z plane...

I first thought magnetic, but that only makes sense for ml, they're both projections though, does anyone know what they stand for? Thanks!

Hi. I read some basic cosmology where it is always said that density fluctuations, pertubations can be described in modes of waves. In particular if you use linearised theory where δ(x,t) is Fourier transformed δ(k,t). What exactly is the reason for this? What do the wave modes describe...

Homework Statement Compute how many n-digit numbers can be made from the digits of at least one of {0,1,2,3,4,5,6,7,8,9 } Assume, repetition or order do not matter. Homework Equations ## a_{1}, a_{2}, ..., a_{n} ## The Attempt at a Solution 10 choices for the 1st sub-index, 10 choices for...

Why are prime numbers important in real life? What practical use are prime numbers?

Why are prime numbers important in real life? What practical use are prime numbers?

(9x)^-1/2 So, I'm not entirely sure how to go about this question. It's got a negative exponent, so I assume its 1 / something. My guess for the answer would be: 1 / 3x [(25xy)^3/2] / x2y For this question, would I compute 253/2 and then x3/2 y3/2 and then divide by x2y

Determine the positive numbers $a$ such that \sqrt[3]{3+\sqrt{a}}+\sqrt[3]{3-\sqrt{a}} is an integer.

Okay, this might be a weird question and I am not sure which sub-forum it belongs to - Math, biology or here. We have this concept of more or less. Given two quantities, we can see whether they are equal, more or less. So we assign each quantity some number, symbol to address it. Similarly...

$a,b,c,d,e,f,g \in N$ $a<b<c<d<e<f<g$ $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{1}{d}+\dfrac{1}{e}+\dfrac{1}{f}+\dfrac{1}{g}=1$ please find one possible solution of a,b,c,d,e,f,g (you should find it using mathematical analysis,and show your logic,don't use any program)

Homework Statement Consider a vector z defined by the equation z=z1z2, where z1=a+ib, z2=c+id. (a) show that the length of z is the product of the lengths of z1 and z2. (b) show that the angle between z and the x-axis is the sum of the angles made by z1 and z2 separately. The Attempt at a...

I have seen a lot of examples of sets with same cardinality as the natural numbers. For instance the even numbers or the cartesian product. In any case the proof amounted to finding a way of labeling the elements uniquely. But I am curious - can anyone give me an example of a set, where this...

I have a view of complex numbers and the way they are taught. I think the whole concept of i as the sqrt(-1) is a terrible place to start. And calling it "imaginary" is worse yet. They should be called blue numbers, or vertical numbers, or something. They are anything but imaginary. It is...

Hi, I'm doing a mini-project in java that involves some nasty calculations with complex numbers- particularly with complex numbers in exponents. Thus far, I've had success using this class: Complex.java . The problem that I'm encountering involves taking the natural logarithm of a complex number...

I imagine most everyone here's familiar with the proof that there's an infinite number of primes: If there were a largest prime you could take the product of all prime factors add (or take away) 1 and get another large prime (a contradiction) So what if you search for larger primes this...

The commutator of two operators A and B, which measures the degree of incompatibility between A and B, is AB - BA (at least according to one textbook I have). But multiplying/substracting matrices just yields matrices! (http://en.wikipedia.org/wiki/Matrix_multiplication). So firstly, how can a...