Thread: Cauchys Integral Formula

Hi, I am fine with solving simpler questions involving Cauchys Integral Formula, but for a couple here I've got stuck. I think my problem is actually with algebra more than anything else, so if anyone could help me i'd be grateful!

The question asks to use CIF to evaluate the integral (contour) of:

(exp (i pi z)) / (z^2 +4)(z^2 -4)

With the contour gamma(t)= 9i + 8exp(i t), 0<t<4pi.


And similarly for:

(cos (z)) / (z^4 +4)

I know I need to rearrange the integral for it to equal f(z) / z - w, but I simple can't figure out how!

Sorry for the crude notation, and thanks.

Originally Posted by rak

[snip]
The question asks to use CIF to evaluate the integral (contour) of:

(exp (i pi z)) / (z^2 +4)(z^2 -4)

With the contour gamma(t)= 9i + 8exp(i t), 0<t<4pi.
[snip]

The singularities of are and . The given contour only encloses .

Therefore you need to calculate where .

Originally Posted by rak

The question asks to use CIF to evaluate the integral (contour) of:

(cos (z)) / (z^4 +4)

With the contour gamma(t)= 9i + 8exp(i t), 0<t<4pi.

Does the given contour enclose any of the zeroes of ....?