Mathematics

I have no clue how to do this one... let a= -1+i, b=-2-i, solve for z. b*=complex conjugate of b z-b*=Im(a^2/(2b+i))

can someone explain how it expands or contracts on a complex plane? The first time i tried to see how it works, i used real numbers, but is there a difference or am i doing something wrong because the triangles as a result are not similar.

What do you think about this podcast from the American Military university?

hey, im a freshman in highschool, so im barely educated in too much complex math, but i want to learn it all{ i know, big statement}. im in an algebra 1 class right now. any good book suggestions teaching this to calculas math? or anything higher than calculas? thanks.

Let us work in the [math]\mathbb{Z}_{2}[/math] graded category. A Loday algebra is a "crippled" or "wonky" Lie algebra. That is it satisfies the bracket satisfies the Jacobi identity, but is not skew symmetric. An interesting question is if there exists a homotopy version. I suspect that one can consider "crippled" [math]L_{\infty}[/math] -algebras. So, a series of brackets that satisfy higher Jacobi identities, but do not have a symmetry property. Any body seen anything like that? A differential over such an algebra would also be straight forward to define. I myself have defined notions of a differential [math]L_{\infty}[/math]-algebra and a differen…

first of this is part of my assignment , secondly please forgive me if i posted this in the wrong place.... this just seemd like the place to post this. i have 2 curved graphs S and V..... and one is increasing more rapidly than the other over a distance at one points in the graph and the other after a few values starts to increase faster than the other one. how would i find the values for the distance where S Gradient is ascending faster than V, and when V Gradient is ascending faster than S...... i only need a push in the right direction please.... i hope i said that coherently . my teacher said to use change in y/ change in x or something but im lost really..…

Hey all, The title's a little misleading, what I'm really wondering about is, can a cube and a cuboid have the same areas AND volumes, without the trivial solution of a=b=c=s, where s is the side of the cube. I did some calculations, however I have absolutely no idea if they're right, and to be quite honest I sort of doubt it. If a, b and c are the sides of a cuboid, and s is the side of a cube, this is what I came up with: http://i44.tinypic.com/oi9e75.jpg Cheers, Gabe

An Elementary Proof Of Both The Beal Conjecture And Fermat's Last Theorem. By: Don Blazys The Beal Conjecture can be stated as follows: For positive integers: [math]a, b, c, x, y, [/math] and [math]z[/math], if [math]a^x+b^y=c^z[/math], and [math]a, b[/math] and [math]c[/math] are co-prime, then[math]x, y[/math] and [math]z[/math] are not all greater than [math]2[/math]. Proof: Letting all variables herein represent positive integers, we form the equation: [math]c^z-b^y=a^x[/math].__________________________________________________________(1) Factoring (1) results in: [math]\left(c^\frac{z}{2}+b^\frac{y}{2}\right)\left(c^\frac{z}{2}-b^\frac{y}…

I am trying to prove [math] \vec{a}\cdot \vec{b} = |\vec{a}| |\vec{b}| cos \theta = a_1b_1+a_2b_2 [/math] in two dimensions. I have come to the conclusion that I need to express the area of a parallelogram spanned by the two vectors [math] \vec{a} = [a_2; -a_1] [/math] and [math] \vec{b} = [b_1; b_2] [/math] by their coordinates. So far I have tried to express the height of the parallelogram in terms of these coordinates, but I have not succeeded. Can you help me further?

What exactly IS continuous compoudning? Anyone know?

It seems hard to find algorithms on the web for computing functions like erf() and zeta() etc. Many sites offer algorithmic solutions at a cost, but my project is non profit so I don't want to spend money on it (it will be released free of charge as a web application). So I am wondering if anybody knows a good algorithm for computing these functions for general complex numbers expressed as (a+bi). The ideal algorithm will be one that is iterative or recursive allowing an arbitrary level of accuracy, and solutions that converge quickly. Right now I need 'erf', 'zeta' and 'gamma' (I have one for gamma but it only calculates real arguments). Other popular special…

Given z is a complex number: a+bi, the function real is defined as real(z) = a; For my purpose this is not satisfactory, I cannot break z into its real and imaginary parts. I am wondering if it is possible to express the function in terms of elementary functions: +, -, *, /, ^, cos, sine, log, exp.... Only z or constants must be used as paramaters to these functions, never a or b. Other functions that break z up cannot be used, for example: real(z) = z-imag(z) is not a valid solution. My gut feeling tells me this is impossible, I would greatly appreciate a solution or verification that there is none. Thanks a lot! - Moosie

I was wondering what the theoretical area of contact between two touching spheres would be. After thinking about this for some time I've come to the conclusion that they would basically meet at a single point, much like a tangent to a circle on a cartesian plane, and whatever little information I could find related to this on the internet supports this. Although, apparently, a 'point' has no actual size. I'm finding this hard to come to terms with- if two spehere met at a single point, which technically has no area or magnitude, how are they touching? Wouldn't they have a shared area between them, even if the area was only one atom?

Does such a thing exist? I think the highest perfect number so far was calculated at 10^300 and mathematicians are currently moving towards 10^500.. so far all perfect numbers are even... Do you think odd perfect numbers exist? I did a few calculations of my own... and thought about it quite a bit and I think it could be done.... it would take an infinite amount of time to calculate the exact number but maybe if you could figure out "about" where it is.. the perfect-number pattern which is....(after the main number of course) "6,8,6,8" adds to itself every consecutive, but it also jumps around a bit to. Another question I have is, are numbers themselves capable of pe…

Hi , I am working on some math stuff and I need to check some points , so are theses formulas correct ? ISZ(x) : is it 0 ? isz (x) = cos ( pi * ( (2*ceil( abs(x) ) + 1)) / 2 ) / cos(1) Ins : Real number x Out : 1 if x=0 , 0 if x <> 0 --------------------------------------------------------------- SGN(x) : Sign sgn(x) = abs(x) / ( x + isz(x) ) Ins : Real number x Out : 1 if x>0 , 0 if x = 0 , -1 if x < 0 more here Dirbax thanks

At the present I'm a math student and study one time a week in order to improve my current math studies. I want to be ambitious, but I have had difficulties and I often finds other things more interesting: http://picasaweb.google.com/khelben1979/Matematik# I would like your opinions on these so called math notes, they are not intented for a high quality presentation. They illustrate my current work with my studies and some of my problems. And please, only nice comments.

how do I work out the mean from these figures?

i can't picture it in my head of how it looks like. I see a front view of it in the book "The Road To Reality" by Dr. Roger Penrose. The picture is a woodcut by M.C Escher called circle limit I. http://math.slu.edu/escher/upload/thumb/e/e5/Circle-limit-I.jpg/200px-Circle-limit-I.jpg So i was thinking how the universe of hyperbolic plane is round and nothing outside of the circle is existent. But i wondered how it would look like from the side or will it be the same as the way i am looking at it right now? Or will it look like a curve with an opening with two lines consisting of it that extends infinitely.

Been a long time since the university years, no books on hand, and with terminology in another language, this may be hard to explain/ask... From a fixed point of view, say the tip of your tv antenna at the roof; -The street hydrant is at a fixed direction; elevation and azimuth. Do not care about the distance. -The sun is at another direction; elevation and azimuth. How is the (bisectriz) bisecting vector elevation and azimuth calculated ? Simply sums divided by 2 ?

When does the generic equation of the 2nd degree not represent a conic section or does it always represent a conic section (unless it has no possible solutions in real numbers)? The other topic I would like like to devote this thread to is families (or sometime called pencils) of conics. [math] C_1 + \lambda C_2 = 0 [/math] represents the zero sets of the family of conics passing through the intersection points of conics [math] c_1 and c_2 [/math] please note that [math]\lambda[/math] is a parameter and assumes all possible real values. [math] C_1 + C_2 = 0 [/math] is the same as the logical operation of this must satisfy both [math] C_1 AND C_2 = 0[/math].howe…

It is an old question, it says: In a gambling game, there are three door numbered #1,#2 and #3. There are a car behind one of the doors. If you guess the right door number, you can get the car. Then you made a guess, say door #1, then the host opened the door3, it turned out to be empty. Then he offered you a change to guess again. The question is " should you change your choice to #2?"

Show that: if the sum of the digits of a natural number N is divisible by 3 then 3 | N.

Hey all, I was wondering the other day, if you rotate the plot of [math]y=x^2[/math] 90° CW, you get [math]y^2=x[/math]. What happens when you do the same with [math]sin(x)[/math]? In other words, which function looks like this: Cheers, Gabe

What is the total sum of all numbers? zero?

Hi everyone, I have some homework to do and ive been asked the following question....... a) Construct an internally and externally calibrated calibration graph. This must be done using Excel and also using graph paper and a pencil (i.e. four graphs are required). my question is what is the difference between an internal and external calibration graph? I have the data. Any help will be much appreciated