Complex variables Definition and 112 Threads

I have to prove that tan^(-1)(z) = i/2 * log[(i+z)/(i-z)] Homework Equations sin^(-1)(z) = -i * log[iz + (1-z^2)^(1/2)] cos^(-1)(z) = -i * log[z + i(1-z^2)^(1/2)] The Attempt at a Solution I've tried a number of attemps. I first tried the most obvious and I did sin^(-1)(z)...

Greetings, I'm working (playing) on a problem involving approximating the arcsin() function. I've attmpted to verify the known derivative of the arcsin function (d(arcsin))/dx = 1/sqrt(1-z^2) I know I have a mistake in my derivation. I've attached an electronic copy of my work...

how to solve two equations involving complex variables?? Hi guys! well! i want to know how can u solve the following two equations simultaenously in order to find out Ix and Iy: (3+j4)Ix - j4Iy=10-------------(1) (2-j4)Ix +j2Iy=0---------------(2) please tell me the best methods to...

I'm wondering if anyone can recommend a good intro to complex variables book for an undergrad (calc1-3,diffeq). Preferably something that can be found cheap on amazon (Dover?)

I am proving that the function f(z) = Arg z is nowhere differentiable by using the definiton of a derivative. I let z = x + yi. Then, if the limit exists, we have f'(z) = lim (/\z -> 0) ( f(z + /\z) - f(z) ) / /\z. (Note that /\ is the triangle symbol) Also, let /\z = p + iq, where p and...

I am majoring in EE and have the option of taking either of these classes. I have to take Calc 1-3, Ordinary DiffE, and Linear Algebra. So after these classes is PDE or Complex Variables more useful to electrical engineers?

Hey all, great site and I look forward to contributing more. For now, a question... For next semester I need to choose between Number Theory or Complex Variables. I am under the impression that complex variables will be the more useful class for my physics education, however I had some concerns...

need some urgent help with basic complex variables (no proofs) Hi: can someone give me examples of the following? (no proofs needed) 1. a non-zero complex number z such that Arg(z^2) "not equal to" 2 Arg z 2. a region in C which is not a domain 3. a non-empty subset of C which has no...

I just signed up to take Applications of Complex Variables next term and wondering if anyone here has the scoop on it. Mainly, what are the main topics and any advice on the class or important parts I should really pay attention to.

How do I solve the following integral using complex variable techniques The integral from 0 to infinity of [x^m/(x^2 + 1)^2]; 1<m<3

So how would one solve the following integral using complex variables?, Integral from 0 to pi of [dx/r +5cos(x)] where 0<r<5

I have several questions on complex variables, so I will just put them all in here. 1. What are the positions and natures of the singularities and the residues at the singularities of the following functions in the z-plane, excluding the point at infinity...