How to compute the integral over these curves

Question

Here is my problem :

compute $$\int_{\mathcal{C}} \frac{1}{z-2i} \,\mathrm{d}z,$$ and $$\int_{\mathcal{C}} \frac{1}{z-e^{i\pi/4}} \,\mathrm{d}z,$$

where,

$C(t) = t$, $t\in[0,1]$

$C(t) = 1 + (t-1)i$, $t \in [1,2)$,

$C(t) = 3 - t + i$, $t \in [2,3]$

$C(t) = i(4-t)$, $t \in [3,4]$

I find that it will be complicated if I try to calculate directly. But, for those cases, I think that I can use Caushy-Gorsat Theorem. So, the answers for these integral will be equal to 0. Is is correct answer?

Answer 1

For the 1st one it is my impression that CG will work, because 2i is not inside the interior of curve, but the 2nd one e^(ipi/4) = 1+i, which lies in the interior of the curve.