Find the countour integral of $\int_{γ} \sqrt{z} dz$ where $γ=C(2,1)^+$ or $γ=C(1,1)^{+}$ or $γ=C(0,1)^{+}$
With $\sqrt{z}$ I mean the branch with the non-positive real axis as branch cut. With $C(a,r)^{+}$ I mean the circle with center $a$ and radius $r$, with $+$ I mean that the circle is postive orientated (counter clockwise).
My effort:
I think for $γ=C(2,1)^+$ I can just use Cauchy's theorem.
For $γ=C(1,1)^+$ I can't use that theorem, and I'm don't know how to evaluate this integral:
$\int_{0}^{2π} \sqrt{|1+e^{it} | } (1+e^{it}) ie^{it} dt$
For the last one $γ=C(0,1)^{+}$, $\sqrt{z}$ is not continuous at this curve (at $-1$), so therefore it's not defined. Right ?