申論題

16.  Let $f(z) = z^{(-1+i)}$ and $C$ be the positively oriented unit circle $|z| = 1$, and we'd like to compute the contour integral $\int_C f(z) dz$.

(b) Since $f(z)$ is a multiple-valued function, let's consider the branch $|z| ＞ 0$ and $0 ＜ \arg z ＜ 2\pi$. When denoting $M := (-1+i)^i$, please use $M$ to express $\int_C f(z) dz$.