A complex integral is a type of integration that involves functions of a complex variable. It is similar to the standard integral in calculus, but instead of integrating over real numbers, it integrates over complex numbers.
Poles of integration outside the curve refer to points in the complex plane where the function being integrated has a singularity or is undefined. These points lie outside the curve of integration and can affect the value of the integral.
Poles of integration outside the curve are important because they can lead to the integral being undefined or having a different value than expected. They also affect the convergence of the integral and can change the path of integration.
Poles of integration outside the curve can be handled by using the residue theorem, which states that the value of the integral is equal to the sum of the residues of the function at its poles. The residues can be calculated using complex analysis techniques.
In some cases, poles of integration outside the curve can be avoided by carefully choosing the path of integration. However, in other cases, they are unavoidable and must be taken into consideration when evaluating the integral.