Hello.
I want to pay up to 2500fg vs 3 math exercis:

1. complex integral curvilinear

2. little proof

3. Exercise about Cauchy’s integral theorem


Rules:
1. The exercise must be described step by step.
2. I have to understand something and have to be confirmed by my mentor.
3. The payment will be divided into two parts. First for making it and the second after my mentor accepts them.
4. If there is a tiny mistake somewhere, the payment will be reduced


If you want to see examples, write a private message

Post problems here, get free answers...

Please PM me

Don't, I'll do it for free

1. Prove that @ Integral from gamma, of function z/((z^2)+1)^2, =0 @ if gamma is a closed patch in C \{+ - i}


2. Prove that if gamma is a contour limiting area D, then the number 1 / (2i) times the integral of the gamma from the function of the conjugated dz is equal
area D. Area. I suggest that you have to go on a curvilinear integral directed real.

3. Determine value of @integral from sigma * K (0,1), of function 1/(z-a)(z-b)@ when
a) |a|, |b| <1
b ) |a| <1 , |b| > 1
c) |a|, |b| >1

Via pm i will give a photo from the book

This post was edited by Dizzien on Jun 24 2018 01:50am

For the first one, this should work I think although it's still a good idea to check for typos, since it's hard not to make mistakes while writing on a computer screen

The basic idea is : for any path that does not enclose singularities, the integral is 0, else, apply the residue theorem, and you still get 0 since the residues happen to be 0

(2.3 -> exercise number you sent me)



I'm looking at the other ones

This post was edited by Hanako on Jun 24 2018 04:48am

For the last one, assuming K(0,1) is a disk centered at 0 of radius 1 (I'm not familiar with this notation)

For the second one, use Green-Riemann's theorem (if you know it, or copy and paste its proof) then it's pretty easy

*Erratum that was pointed out to me by OP for anyone wondering (forgot an exponent in the denominators) :

Man... I wanted some fgs