The residue theorem part 1 | Complex Analysis | LetThereBeMath |

The residue theorem is extremely useful for evaluating complicated contour integrals by using concepts similar to Cauchy’s theorem. It is also useful for finding the inverse Laplace transform and the inverse Z-transform, both of which have important applications in signal analysis.

[vepadilla]

When do we know to appropriately apply Residue theorem or Cauchy's integral theorem. They seem to do the same thing, it just seems they are different tools. I would assume in certain circumstances one is faster to retrieve an answer from though, is there a way to know without applying both to a problem?