I am doing a problem of a contour integral where the f(z) is z1/2. I can do most of it, but it asks specifically for the principal root. I have been having troubles finding definitively what the principal root is. Anyplace it appears online it is vague, my book doesn't speak of it, and my professor mentioned it in passing, so I have these two questions:
1. Is the principal root the branch of the root where the argument of the 2nd root is where k = 0 for it being y/2 + kπ?
2. Should I take the principal root before or after the integration? Will it make a difference?