I know the procedure of computing contour integration of a given complex function using cauchy's lemma's rule.But,I am confused about when to use cauchy's-lemma 1 and when caushy's-lemma 2 or jordan's-lemma. Please help me understanding that.please be as simple as you can.
My Assumption: If the poles stay in the region of the semicircle but outside the real axis(means ,if the singular points are imaginary) ,then we have to use lemma 2 (big semicircle). But,if the pole stays on real axis ,then I have to use Lemma 1.Is it right?