Recent content by SALAAH_BEDDIAF

Okay, so I have all the roots now, as these roots are very difficult to be represented by fractions, can I use the approximate roots to find the residues or will I have to use the exact value?

so the roots of (x^4 + x^3 + x^2 + x + 1) are also the remaining roots of (x^5-1)?

So I understand I will be evaluating this integral using Cauchy's Residue Theorem so I must find the singularities in the function, this is when (x-1)(x^4 + x^3 + x^2 + x + 1) = 0 , from (x-1) we get a singularity to be 1, but I'm having difficulty finding (x^4 + x^3 + x^2 + x + 1) to be 0

Homework Statement Show that \int_{-\infty}^{+\infty} \frac{x-1}{x^5-1}dx = \frac{4\pi}{5}sin(\frac{2\pi}{5}) The Attempt at a Solution This is actually a piece of work from a complex analysis module (not sure if it belongs in this part of the forum or in the analysis section) I...

But from the substitution, wouldn't the limit of 2\pi become 0? Both points give us a value of 0 as tan(0) = tan(2\pi)

https://www.dropbox.com/s/06om29hdi2p6ikt/20131129_165002.jpg

Thanks, but on my course we don't use any sort of expansions so I'm having difficulty understanding what the expansion actually tells me, I just wanted to know if those singularities I have are just simple poles or poles of higher order.

\int_0^{2\pi} \frac{1}{25cos^2(t) + 9sin^2(t)}dt Substituted the variables twice and got the upper and lower boundaries to both be 0 (think i might have gone wrong there) \frac{1}{15} tan^{-1} \frac{3tan(t)}{5} with upper and lower boundaries both being 0. I know the answer is 2\pi/15...

Hi guys, just wanting to know if I'm doing this right. f(z) = \frac{z}{(z^2 + 4) (z^2+1/4)} Singularities of f(z) are when (z^2 + 4), (z^2 + 1/4) = 0 In this case, the singularities are \pm2i , \pm\frac{i}{2} Lets call these singularities s and s is a simple pole if \lim_{z...

Let f(x+iy) = \frac{x-1-iy}{(x-1)^2+y^2} first of all it asks me to show that f satisfies the Cauchy-Riemann equation which I am able to do by seperating into real and imaginary u + iv : u(x,y),v(x,y) and then partially differentiating wrt x and y and just show that \frac{\partial...

[SIZE="4"]okay i got i_1 + i_2 + i = i_s (t) using the equalities v = iR = L\frac{di}{dt} = \frac{Q}{C} I got i_1 R = L \frac{di}{dt} → i_1 = \frac{L}{R}\frac{di}{dt} not too sure how to transform C\frac{dv}{dt} → LC\frac{d^2 i}{dt^2}

I think i may have got it? here is what i have Current through resistor: \frac{1}{R} Current through inductor: \frac{1}{L} \int i\,dt Current through Capacitor: C\frac{dv}{dt} Applying kirchhoffs law i got \frac{1}{R} + \frac{1}{L} \int i\,dt + C\frac{dv}{dt} = 0...

no I'm able to solve the equation, it's just that I'm ahving difficulty showing that the equation equals what i have given

Homework Statement Hi there guys I am new to this forum and i have a problem with a bit of cw. It's regarding an RLC circuit. I've come up with a picture (attached) that denotes the equation. Homework Equations I know the equation is L C \frac{d^2 i}{d t^2} + \frac{L}{R} \frac{di}{dt}...