How to evaluate $$\oint_{C}z^idz $$ over a unit circle in complex plane.
I tried following.
t = angle theta
$$z = e^{it}$$
$$z^i = i \operatorname{Log} z = i \operatorname{Log} (e^{it})= i i t= - t$$
$$dz = i e^{it} dt$$
$$-i\oint_{C}te^{it}dt$$
Sorry for plain text, I dont know how to type math