Recent content by soulsearching

i did not get Pere Callahan's method. and why did you choose the contour as z=1/2? the question says integrate it around z=1

I think its going to be 2pi(i) because the singularity (1/2) is inside the contour. is this right?

Like after breaking up the fraction into 3 fractions using partial fractions, what's the next step? Thanks... :)

We haven't covered residue theorem yet. Is there any other way to solve it?

Also when trying to find the integral of (1/8z^3 -1) around the contour c=1. I found the singularities to be 1/2, 1/2exp(2pi/3), and 1/2exp(4pi/3) What is the next step here. Do I just assume the integral is 6pi(i) after using partial fractions to find the numerators of the 3 fractions...

Also when trying to find the integral of (1/8z^3 -1) around the contour c=1. I found the singularities to be 1/2, 1/2exp(2pi/3), and 1/2exp(4pi/3) What is the next step here. Do I just assume the integral is 6pi(i) after using partial fractions to find the numerators of the 3 fractions...

Thanks Dan.

So the point z = 5 is outside the contour, so the integral vanishes right? Thank you Tim. When trying to show the same for this equation here around the same contour f(Z) = (4z^2 -4z +5)^-1 I found the singularities here to be (1/2 + i) and (1/2-i). Is the integral zero because...

Can anyone help me with this pls? How can you prove that the integral of f(z) around the contour z= 1 is 0 where f(z) is Log(z+5) Thx I know Log(z) is ln r + i (theta). But i don't know how that applies to this situation. Also, do I solve it as a normal integral or use...