You're certainly OK if it does not include any of those, but maybe by including some combination of them you would still get zero. Not sure whether the question expects you to consider that.dla said:The curve can't include z=±4i and z=0
Contours are curves or paths on a graph that are used to evaluate integrals. They are typically used in complex analysis to simplify integrals and help find their values.
Not all contours will result in an integral equaling 0. The contour must meet certain criteria, such as being a closed path and not containing any singularities, in order for the integral to equal 0.
This will depend on the specific integral and function being evaluated. In general, a contour can be chosen so that the function being integrated is simpler or has more symmetry, making the evaluation easier.
Yes, it is possible to use multiple contours to evaluate an integral and make it equal 0. This is often done when the function being integrated has multiple singularities or complicated behavior.
Contour integration can be a powerful tool, but it does have its limitations. It may not always be possible to find a contour that results in an integral equaling 0, and even when a contour can be found, it may not always be the most efficient or accurate method of evaluation.