Serious help needed with complex variables

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.

We know that d/dz (zlog(z) - z) = log(z).

If this is true then the integral of log (z) is zlog(z) - z.
You have the points so:

[z1log (z1) - z1] - [z2log (z2) - z2]

where z1= 1 + i and z2= 1 - i