- #1
mikethemike
- 6
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Homework Statement
Notation: C=complex plane, B=ball, abs= absolute value, iff=If and only if
Given z0 in C and r>0, determine the path integral along r=abs(z-z0) of the function 1/(z-zo).
2. The attempt at a solution
It seems to me I'm being asked to find the value of a path integral (a circle) under a function. So using Cauchy's Theorem implies it is zero iff f is holomorphic. This means I must prove the function is holomorphic, which leads me to the question, what is the difference between a holomorphic function, and one that is continious, and how do I go about illustrating this?
Should this function not be continous, I could use the fact that the initial point of the path integral is equal to the final point and come up with an equation based on primatives.
Any help would be appreciated, as I feel I'm just on the cusp of understanding this stuff.
Thanks,
Mike