Complex analysis Definition and 756 Threads

Cauchy integral question The question calls for finding the integral of dz/((z-i)(z+1)) (C:|z-i|=1) I can't figure out how to do this for (C:|z-i|=1). How does this differ from, say, (C: |z|=2) Regards

Here's a problem I ran into in complex analysis. Given z = x + iy and w = u + iv, I need to find all w such that w² = z. It reduces to solving this system: x = u² - v² y = 2uv My professor mentioned that we should try to deal with the problem in at least two cases: y = 0, and y does not...

Hi people, I'm Joseph, 17, English studying European Baccalaureate. I was wondering if anyone here could recommend for me a good introductory book on Complex Analysis that requires only an understanding of the complex numbers you would cover in High School Maths. Maybe something...

Anyone know how to find a sum of a function using the poisson summation formula and the Fourier transform. Thanks! --yxgao

More "Complex" Complex Analysis I have another problem that has eluded me for days and I'm sure I'm close. If anyone can help, please nudge me in the right direction. Consider the mapping w = u + iv = 1/z, where z = x + iy. Show that the region between the curves v = -1 and v = 0 maps into...

I am having trouble with the following question, any help would be blinding. Find the value of ther derivative of: (z - i)/(z + i) at i. I tried to use the fact that f'(z0) = lim z->z0 [f(z) - f(z0)]/z - z0. I also tried using the fact that z = x + iy and rationalising the denominator...