Complex Definition and 1000 Threads

Homework Statement I have the answer to this question, but I'm trying to understand how to do it. It's a simple circuit: https://onedrive.live.com/redir?resid=6CDEB7909E9460BA!57382&authkey=!ALscxM1v2OtHZIg&v=3&ithint=photo%2cPNG (note: Image inserted in-thread by moderator) The questions...

In my electrical engineering textbook, they have an entire chapter devoted to the complex Exponential. I don't really understand it, nor do I understand its importance. I know it is extremely important, and need to understand why, and what exactly it is, and the wording of the online resources...

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...

Hi friends, I am looking for a good book on complex analysis. My goal is to add some new techniques to my problem solving arsenal, learn some elegant non-intuitive proofs and finally build up to knowing enough about the Zeta function to understand it's relationship with prime numbers.

Is it possible to get Maple to show me step by step how to solve a complex contour integral? f := (x,y,z,v) -> (x+I*x*cos(v)+I*y*sin(v))^(-2) int(f(x,y,z,v),v=0..2*Pi) assuming(x,real,y,real,z,real,v,real) But I would like to know how Maple solves this step by step. I tried using the tutor...

Homework Statement Finding "polar" and "rectangular" representation of a complex number? Make a table with three columns. Each row will contain three representations of a complex number z: the “rectangular” expression z = a + bi (with a and b real); the “polar” expression |z|, Arg(z); and a...

Hi, I have a difficult time trying to perform the following integral, $$ j({T}, \Omega)=\int_0^{ T} d\tau \frac{\tau^2\exp(-i\Omega\tau)}{(\tau-i\epsilon)^2(\tau+i\epsilon)^2} $$ The problem is that the poles ##\pm i\epsilon## when taking the limit ##\epsilon\rightarrow 0## are located at...

Homework Statement A real voltage source can be expressed as an ideal voltage source that is in series with a resistor that represents the inner resistance of the voltage source. This voltage source is a EMF and it is also in series with another resistor. Suppose both the EMF resistor...

How would you go about solving (4(x^3)+38(x^2)+44x-20)/(20+12x+x^2), without the use of a computer, further, what about functions which have more x components, with higher powers. Also what process do computers use to solve these.

If I have an normalized spin superposition |ψ> = (a1+a2i) |1> + (b1+b2i) |2>, and asked to write it in the form |ψ> = cosθ|1> + eiΦsinθ|2>, how do I proceed? My main problem is that no matter what I try, I can't seem to get rid of some complex component that shows up in the coefficient of |1>...

Homework Statement An 82 kg man drops from rest on a diving board 3 m above the surface of the water and comes to rest .55 s after reaching the water. What is the net force on the diver as he is brought to rest Homework Equations FDt = mv F = mg v^2 = vi^2 = 2aDx Dx = 3m Dt...

I am rather new to the whole idea of complex conjugates and especially operators. I was trying to understand the solution to a problem I was doing, but the math is confusing me rather than the physics. In the last row of calculations, why does the sin change to a cos, and the d/dx change to...

I find this interesting. You can approximate pi/4 with the Gregory and Leibniz series pi /4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 ... (1) btw it takes a lot of terms to get a reasonable approximation for pi. The formuli is pi / 4 = [ ( -1 ) ^ ( k + 1 ) ] / ( 2 * k -1)...

I am trying to teach myself complex analysis . There seems to be multiple ways of achieving the same thing and I am unsure on which approach to take, I am also struggling to visualise the problem...Would someone show me step by step how to solve for example...

z1,z2,z3 are distinct complex numbers, prove that they are the vertices of an equilateral triangle if and only if the following relation is satisfied: z1^2+z2^2+z3^2=z1.z2+z2.z3+z3.z1 so i shall show that |z1-z2|=|z1-z3|=|z2-z3|but i do not know how to start.

Homework Statement A combination circuit powered by a 6.0 V battery is shown. What is the total current through this circuit? I don't know how to determine where the signs go, for example if the right side of a resistor is positive or the left side is positive Homework Equations What is the...

Hello, folks. I'm trying to figure out how to take the partial derivative of something with a complex exponential, like \frac{\partial}{\partial x} e^{i(\alpha x + \beta t)} But I'm not really sure how to do so. I get that since I'm taking the partial w.r.t. x, I can treat t as a constant term...

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...

Function kind of cross between a helicoid and a complex plane wave? I would like to translate a mental picture into a mathematical expression if possible. The picture might be roughly thought of as a cross between a complex plane wave and a helicoid. A construction I think goes as follows, take...

Is the basis vector ##(i,0,1)## in the space ##V=##Span##((i,0,1))## with a standard inner product,over ##\mathbb{C}^3## orthogonal to itself? ##<(i,0,1),(i,0,1)> = i \cdot i + 0 \cdot 0 + 1 \cdot 1 = -1 + 1 = 0 ## The inner product (namely dot product) of this vector with itself is equal to...

My friend told me the 2 24 are shorted. How do I know these are shorted and b) what do I do do make this question simple?

anorlunda submitted a new PF Insights post The Case for Learning Complex Math Continue reading the Original PF Insights Post.

Homework Statement How would one go about finding the antiderivative to this function? Homework Equations N/A The Attempt at a Solution This problem has been rather tricky I have tried several attempts at the solution. My one solution consists of me factoring out the x^4. Looking for some...

Homework Statement Homework Equations Kirchoff's Current and Voltage laws The Attempt at a Solution How do you go about analyzing a complex circuit like this? Do you just write out the current equation for each highlighted junction and voltage equations for each loop? Is there a quick way...

Isaac0427 submitted a new PF Insights post Complex and Irrational Exponents for the Layman Continue reading the Original PF Insights Post.

Homework Statement a) Solve equation z + 2i z(with a line above it i.e. complex conjugate) = -9 +2i I want it in the form x + iy and I am solving for z. b) The equation |z-9+9i| = |z-6+3i| describes the straight line in the complex plane that is the perpendicular bisector of the line segment...

Hello, I was wondering how well is Rudin's Real and Complex Analysis for learning complex analysis, assuming that difficulty won't be an issue. Does it cover the standard material? Is it deep enough? Should I just read from elsewhere instead?

Is taking complex analysis before graduate school apps a "make-or-break" deal if one is looking to apply for theory? I am currently deciding whether to take it junior spring or defer it to senior spring. As it has come up in my research, I have studied some of it, but I'm wondering if it must be...

Without the help of calculator, evaluate \frac{(-\sqrt{6}+\sqrt{7}+\sqrt{8})^4}{4(\sqrt{7}-\sqrt{6})(\sqrt{8}-\sqrt{6})}+\frac{(\sqrt{6}-\sqrt{7}+\sqrt{8})^4}{4(\sqrt{6}-\sqrt{7})(\sqrt{8}-\sqrt{7})}+\frac{(\sqrt{6}+\sqrt{7}-\sqrt{8})^4}{4(\sqrt{6}-\sqrt{8})(\sqrt{7}-\sqrt{8})}.

Homework Statement I have the following matrix: 0 0 0 1 1 0 0 0 = A 0 1 0 0 0 0 1 0 and the vector v = (1,0,0,0) If I perform Av, this gives: Av=(0,1,0,0) And If I keep multiplying the result by A like A*A*(Av), the outcome will be something like j= (0,0,1,0) k=(0,0,0,1) l=(1,0,0,0) The...

I found this formula in a paper: \int exp( \frac{x1 + i x2}{ \sqrt 2} \eta^* - \frac{x1 - i x2}{ \sqrt 2} \eta) D(\eta)/ \pi d^2 \eta the author calls it the Fourier transform of D. It is the first time thar i see this formula. How common is this notation? Can we use it without problem?

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... -...

Can an orthogonal matrix involve complex/imaginary values?

In trying to get an intuition for curl and divergence, I've understood that in the case of R2, div f(x,y) = 2Re( d/dz f(z,z_)) and curl f(x,y) = 2Im( d/dz f(z,z_)), where f(z,z_) is just f(x,y) expressed in z and z conjugate (z_). Is there any way of proving the fundamental properties of div and...

In trying to get an intuition for curl and divergence, I've understood that in the case of R2, div f(x,y) = 2Re( d/dz f(z,z_)) and curl f(x,y) = 2Im( d/dz f(z,z)), where f(z,z) is just f(x,y) expressed in z and z conjugate (z). Is there any way of proving the fundamental properties of div and...

micromass submitted a new PF Insights post Things Which Can Go Wrong with Complex Numbers Continue reading the Original PF Insights Post.

Exactly as stated in the title. What does ph(z) mean?

Hello everyone, I have a problem with finding a residue of a function: f(z)={\frac{z^3*exp(1/z)}{(1+z)}} in infinity. I tried to present it in Laurent series: \frac{z^3}{1+z} sum_{n=0}^\infty\frac{1}{n!z^n} I know that residue will be equal to coefficient a_{-1}, but i don't know how to find it.

If $z = e^{(2-\frac{i \pi}{4})}$ what's $z^5$? The only way I can think of doing this is expanding $(2-\frac{i \pi}{4})^5$, but I think I'm supposed to use a simpler method (not sure what it's).

What's the ratio $\displaystyle \frac{e^{i\sqrt{x}}-1}{e^{i\sqrt{x}}+1}$ equal to? I can't work it out to anything I recognize. :confused: The answer is $\displaystyle i\tan(\frac{1}{2}\sqrt{x})$. I suppose I could work backwards from the answer, but I won't have the answer in the exam.

What's the quickest way to calculate the argument of $\displaystyle \pi e^{-\frac{3i\pi}{2}}$?

An old exam question is: Evaluate $ \oint \frac{e^{iz}}{z^3}dz $ where the contour is a square of sides a, centered at 0. This has a simple pole of order 3 at z = 0 Perhaps using residues, $ Res(f,0) = \frac{1}{2!}\lim_{{z}\to{0}}\d{^2{}}{{z}^2}z^2 \frac{e^{iz}}{z^3} =...

An old exam has: Evaluate $ \oint\frac{dz}{z(2z+1)} $, where the contour is a unit circle This look good for the residue theorem, it has 2 simple poles at 0, $-\frac{1}{2}$ $ Res(f, 0)= \lim_{{z}\to{0}}z\frac{1}{z(2z+1)}=1$ $ Res(f, -\frac{1}{2})=...

I am bit confused with the Eueler representation of Complex Numbers. For instance, we say that e^{i\pi}=cos(\pi)+isin(\pi)=-1+i0=-1. The derivation of e^{i\theta}=cos(\theta)+isin(\theta) is carried out using the Taylor series. I quite understand how ##e^{i\pi}## turns out to be ##-1## using...

Is it possible to divide and multiply complex numbers and real numbers and if so, how does one do that? If not, why so? Cheers for your help!

First post ! I hope that my question will not make some long time physicists laugh. It is about geometrical quantization and the phase space in which we use : z=1/sqrt(2)(q+ip) My question is simple what is this 1/sqrt(2) ? And what is it is interpretation ? Thank you !

One problem I sometimes encounter is with complex numbers. When a formula including functions of complex variables runs in Matlab, I obtain the corresponding result but if I write that formula in different forms (for example when I arrange the long formula in simpler form) I obtain another...

For hydrogen atom ground state we know φ=π-1/2a-3/2e-r/1 I want to know the complex conjugate of φ* ?

Homework Statement In the argand plane z lies on the line segment joining # z_1 = -3 + 5i # and # z_2 = -5 - 3i # . Find the most suitable answer from the following options . A) -3∏/4 B) ∏/4 C) 5∏/6 D) ∏/6 2. MY ATTEMPT AT THE SOLUTION We get two points ( -3 , 5 ) & ( -5 , -3 ) => The...

Homework Statement Arg z≤ -π /4 Homework EquationsThe Attempt at a Solution I'm confused whether the answer to that would be more than -45° or less. Should the approach to arguments be the same as in negative numbers?