/sci/ - Science & Math

[Anonymous No.5160412]

morning guys

Would really appreciate if someone would take a look at this problem for a second.

We have <span class="math"> \int_\gamma \frac{dz}{z^2-8} [/spoiler] where <span class="math"> \gamma [/spoiler] is the circle <span class="math"> |z|=2 [/spoiler]. The integral is made trivial by Cauchy's theorem, since the function is holomorphic inside the path. So, the answer is 0. However the question asks us to evaluate the integral using Cauchy's Integral Formula, which is:

<span class="math"> f(z_0) I(\gamma;z_0)=\frac{1}{2\pi i} \int_\gamma \frac{f(z)}{z-z_0}dz [/spoiler]

Does anyone see a way to show this integral is zero by cauchy's integral formula?

thanks in advance

[Anonymous No.5160473]

bump for desperation, apologies

[Anonymous No.5160493]

Are you fucking retarded?

<div class="math">\frac{1}{z^2-8}=\frac{\frac{z}{z^2-8}}{z}</div>

[Anonymous No.5160533]

>>5160493
yes, fuck my life.