Evaluate the line integral log(z) dz

where C is the arc defined by z= root2 x e^(itheta), -pi/4 < or = theta < or = pi/4.

between the points (1-i) and (1+i).

In a domain where log(z) is analytic we know that d/dz (zlog(z) - z) = log(z).

Hence evaluate the above integral directly.