In Reply to: hw 5 no. 13 posted by Connie on February 13, 2000 at 16:50:51:
>Hi, Porf. Tao,
>I was doing hw 5 section 4.4 no. 13 (a), and i simplified the problem
>into (int 1/(z^2+1) along a circle) with i inside inside the circle. Actually,
>i don't know if I have simplified the problem by doing this and I don't know
>how to take the integeral from this point on.
>I wonder if you can help me on this.
>Thanks.
>Connie
There are several ways to approach this problem. The easiest is
to factor z^2 + 1 as (z+i)(z-i) and use the tricks in the Week 5
notes (moving one factor from the denominator to the numerator, etc).
One can also try to play around with branches of the arctangent
function (as it will be an anti-derivative of 1/(z^2+1) in most
places), but I really don't recommend this approach as it is quite
messy and it is very easy to slip up and end with the wrong answer.
Terry