Thread: cauchy's integral theorem

Im attempting to show that the following is not true by cauchy's integral theorem.

where is the unit circle (travelled anti-clockwise).

Resolving i got z = 2 and z = 3 but these singularities lie outside the unit circle...

I know i need to do something with the but cant figure out what

Originally Posted by Tekken

Im attempting to show that the following is not true by cauchy's integral theorem.

where is the unit circle (travelled anti-clockwise).

Resolving i got z = 2 and z = 3 but these singularities lie outside the unit circle...

I know i need to do something with the but cant figure out what

Either it is or you did a mistake in computing the roots.

Anyway, the trick is to notice that, if , then , so you can apply Cauchy theorem and there is a pole inside the contour.

ya sorry about that, it should have been

Thanks for the help