Recent content by desaila

Homework Statement integral of (z^2/(4-z^2)) with respect to z, over |z+1|=2 Homework Equations Cauchy's Formula(I'm attempting to do it in the more fancy and easily readable sense, if it's not readable then go here.. http://en.wikipedia.org/wiki/Cauchy%27s_integral_formula )...

Oh. Well then. You can't use euler's because the function is real valued, correct? Or, can you expand it and just leave off the imaginary part? I can't think of another way to show that this function is going to zero.

Homework Statement Show that the sequence real-valued functions fn(x) = sin(x/n) converges uniformly to f(x) = 0 on A=[0,pi] Homework Equations I don't believe there are any The Attempt at a Solution Well, my first thought was that if x/n = pi then sin(x/n) is obviously going to...

Homework Statement f(z) = (z+1)/(z-1) What are the images of the x and y axes under f? At what angle do the images intersect? Homework Equations z = x + iy The Attempt at a Solution This is actually a 4 part question and this is the part I don't understand at all really. The...

I'm really unsure how to go about graphing a complex function. Like, f(z) = z^2, where z = x+iy. This ISN'T a homework problem, but I'm studying for an exam and that's an example in a book I'm reading and it says "the image of this function" and goes on explaining some things relevant to...

It is old stuff, but I didn't quite understand it then. The conformal mapping theorem, according to the book, is, "If f is analytic in the disc |z-zo|<r and if f'(zo) != 0, then f is conformal at zo." Where zo is z with subscript 0.

Homework Statement "Study the infinitesimal behavior of f at the point c. (In other words, use the conformal mapping theorem to describe what is happening to the tangent vector of a smooth curve passing through c.)" f(z) = 1/(z-1), c=i Homework Equations |f'(c)| and arg f'(c)...

So, Here is one that I think applies to your linearity short-cut you mentioned earlier. Because z+1/z is analytic, then 1/[(z+1/z)^2] must be as well. I'm going to attempt to work it out though.

Yes, that is what I found. I should have been less vague in my edits. This problem is heaps of fun so far. I think my professor is a sadist.

Haha, in terms of explaining something relatively simple in the terms of a more complex problem, yes I am happy. However, that is the problem I'm on now. What's getting me hung up is trying to isolate the real and imaginary parts. the 3-z turns into a trinomial if you substitute in x+yi. I...

Alright, how do you know C-R works without doing all the work? EDIT: I also worked out the equations, and you were correct, the function is analytic. Not that I doubted you, but just saying I seemed to have come to an understanding. I really appreciate the help Dick.

x + i(y) + x/(x^2 + y^2) - i(y/(x^2+y^2)) ? If that's correct, then what you're saying is you need to isolate i in these equations in order to successfully do the C-R equations? I think I just didn't quite understand the C-R equations, is the problem I was having.

When you do that, you get (x+iy) + (x-iy)/(x^2 + y^2) I'm not sure I understand how that helps me? I apologize if I seem slow here, but I'm just not quit seeing this.

Hm, so what you're saying is that you basically just look at the real and imaginary parts.. So when I'm looking at u or v I should drop the i's out? I think I just re-phrased what you said.. How about a slightly more complicated example just to clarify things a bit? Using the same given...

Homework Statement z + 1/z is it analytic? Homework Equations du/dx = dv/dy and du/dy = -dv/dx where f = u+iv The Attempt at a Solution I'm pretty sure I did this correctly, but I ran into an unexpected answer in a more complex problem using the same method and thought I'd...