- #1
MurraySt
- 8
- 0
Thanks in advance for your time and all the wonderful previous answers I've received lurking on this site - its been great!
Anyway I have two functions G:[0,2pi] --> Complex Plane and
H:[0,4pi] --> Complex Plane
Both functions are equal to exp(it). (The complex exponential function w/ argument it).
I am told that these functions are not homotopic over the region C - {0} and asked for a proof.
Another hint is to use Cauchy's Theorem which says that if two curves are homotopic their integrals are equivalent.
Any suggestions?
Anyway I have two functions G:[0,2pi] --> Complex Plane and
H:[0,4pi] --> Complex Plane
Both functions are equal to exp(it). (The complex exponential function w/ argument it).
I am told that these functions are not homotopic over the region C - {0} and asked for a proof.
Another hint is to use Cauchy's Theorem which says that if two curves are homotopic their integrals are equivalent.
Any suggestions?