Complex analysis - integral independent of path

[player1_1_1]

Homework Statement

integral: $$\int\limits_C\cos\frac{z}{2}\mbox{d}z$$ where $$C$$ is any curve from 0 to $$\pi+2i$$

The Attempt at a Solution

can i do this like in real analysis when counting work between two points, just count this integral and put given data in?

 

[HallsofIvy]

Yes, since [math]cos(z/2)[/math] is an analytic function, the integral is independent of the path, so you can just go ahead and integrate, the set $z= \pi+ 2i$ and 0.

 

[player1_1_1]

and then: $$\ldots=\left|2\sin\frac{z}{2}\right|^{z=\pi+2i}_{z=0}=2\sin(\pi+2i)$$ yeah?