Complex Definition and 1000 Threads

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?

Homework Statement Of all complex numbers that fit requirement: ## |z-25i| \leq 15## find the one with the lowest argument. Homework EquationsThe Attempt at a Solution z=a + ib (a, b are real numbers) ## \sqrt{a^2 + (b-25)^2} \leq 15 \\ a^2 + (b-25)^2 \leq 225 ## The lowest possible...

Homework Statement Given n=(x + iy)/2½L and n*=(x - iy)/2½L Show that ∂/∂n = L(∂/∂x - i ∂/∂y)/2½ and ∂/∂n = L(∂/∂x + i ∂/∂y)/2½ Homework Equations ∂n Ξ ∂/∂n, ∂x Ξ ∂/∂x, as well as y. The Attempt at a Solution ∂n=(∂x + i ∂y)/2½L Apply complex conjugate on right side, ∂n=[(∂x + i ∂y)/2½L] *...

Homework Statement Solve the following equation: ## (1+a)^n=(1-a)^n## where a is complex number and n is natural number Homework Equations Euler's formula The Attempt at a Solution I've tried something like this ## (1+a)^n=(1-a)^n \\ (\frac{1+a}{1-a})^n=1 ## But i really have no idea...

hello! 1) what is the process to get the derivative of an equation that requires you to do first the chain rule and then the product/quotient rule, eg. sin(x^2(x+1))? 2) what is the process to get the derivative of an equation that requires you to do first the product/quotient rule and then the...

Homework Statement Suppose that the characteristic equation to a second order, linear, homogeneous differential equation with constant coefficients yielded two complex roots: \begin{array}{l} {\lambda _1} = a + bi\\ {\lambda _2} = a - bi \end{array} This would yield a general solution of: y =...

Homework Statement It is known that roots of complex polynomial: ##P_n (z) = z^n + a_{n-1}z^{n-1} + \cdots + a_1z + a_0## are the following complex numbers: ##\alpha_1, \alpha_2, \cdots, \alpha_n ## Find the product: ##\prod = (\alpha_1 + 1)(\alpha_2 + 1)\cdots(\alpha_n +1)## Homework...

I tried my best but I wasn't able to solve this can someone please provide me with a detailed solution. Here 's the question : Establish the expression of Vs/Ve (complex) using Thevnin's theorem Here is the circuit : I spent 4 hours trying to solve this but I had no clue how. I'am having...

Homework Statement [/B] Find and classify all singularities for (e-z) / [(z3) ((z2) + 1)] Homework EquationsThe Attempt at a Solution [/B] This is my first attempt at these questions and have only been given very basic examples, but here's my best go: I see we have singularities at 0 and i...

I am looking for conformal transformations to map: 1. Disk of radius R to equilateral triangular region with side A. 2. Disk of radius R to rectangular region with length L and width W. 3. Disk of radius R to elliptic disk with semi-major axis a and semi-minor axis b. Thanks!

Homework Statement If a force F = F_0 cos (\omega t) = \Re{\{F_0 e^{i \omega t}\}} is applied to a body of mass m attached to a spring of constant k, and x = \Re\{z\} . Show that the following equation holds: m \ddot{z} = - k z + Fe^{i \omega t} . Homework Equations Newton's second law. The...

The scalar fields of supersymmetric theories in 4 spacetime dimensions are a set of complex fields (usually denoted by ##z^{\alpha}##). How can this be physically translated? More precisely, we know that in 5D, those scalars are real, so what is that makes them real here but complex there?

In general, one thinks of complex numbers as being absolutely required in Quantum Physics but as being optional in Classical Physics. But what about modern classical electromagnetic field theory (gauge theory) in which the electromagnetic field is coupled to the field of charged particles by...

Homework Statement I have the following complex numbers : -3,18 +4,19i I must put it in polar form. Homework Equations r=(a^2+b^2)^(1/2) cos x = a/r sin x = b/r The Attempt at a Solution I was able to find with cos x = a/r that the x = 127,20 But when I do it with sin x = b/r I obtain like...

The conserved 4-momentum operator for the complex scalar field ##\psi = \frac{1}{\sqrt{2}}(\psi_1 + i\psi_2)## is given in terms of the mode operators in ##\psi## and ##\psi^{\dagger}## as $$P^{\nu} = \int \frac{d^3 p}{(2\pi)^3 }\frac{1}{2 \omega(p)} p^{\nu} (a^{\dagger}(p) a(p) +...

Homework Statement The problem states that you need to solve the following equation (without a calculator) : z^5 = z̅ Homework Equations z=a+bi and z̅=a-bi The Attempt at a Solution So far I've tried multiplying both sides by z̅: z̅ * z^5 = |z̅|^2...