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 $\int_C f(z) dz$.

 (a) Let's denote the complex number $(-1+i)^i$ as $\exp(a+ib)$ with $a, b \in \mathbb{R}$. What are $a$ and $b$?