This is a complex analysis question

Compute the path integral / f (z) dz where f(z) = log,(z) and y is the semicircle connecting -i to i in the right half-plane: Im Z 2 0. Hint for e): Recall that log, is a well-defined function on C\\ LT. = C\\[-co, 0] and by definition, log (z) = In(|z) ) + it where t E arg(z) n (n, 3x). At the cost of repetition, this is how we get well- definedness. Then y(t) = ell, t E [3x/2, 5x/2]. Integration by parts might be helpful