Is there a numerical method to solve complex plane integrals?

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SUMMARY

The discussion centers on the numerical methods for solving complex plane integrals, specifically the integral from 1-8i to 1+8i of the function f(z). Participants emphasize that while the integral can be evaluated using residue calculus, the focus is on numerical methods. It is established that the integral is path-dependent, necessitating a defined integration path to obtain meaningful results. The conversation highlights the importance of understanding the behavior of f(z) along the chosen path.

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eljose
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Let be the integral in the complex plane:

Int(1-i8,1+i8)dz/f(z) is there anumerical method to solve it (i know that it could be solved by calculating the residues of f(z) buit my iterest is in knowing if it can be calculated by using some numerical method...thanks)
 
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If you mean integral from 1- 8i to 1+ 8i, then it isn't even well defined. You will need to integrate along a particular path and the result will depend upon which side of any zeroes of f you go on.
 
well the path would be across the real line re(z)=1 here with 8 i mean infinite, now i could solve it by calculating the zeroes of f(z) but i am not intersted in it i am interested in knowing if there is a numerical method to solve it and where could i find it
 

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