I am a little bit confused about using these theorems. For example, if I want to find the value of $\int_C e^{az}/z dz$ given that C is the unit circle with positive orientation, and a is a real number.
Without knowing that if z is inside the circle or outside the circle, does that mean I can't use any of this theorem?
And if I want to use these theorems, first I need to prove that the function is analytic and second its interior is inside the contour? Thanks a lot.