Solving Complex Line Integrals: Line Segment from 2 to 3+i Using Green's Theorem

[loki91]

Homework Statement

Compute the following line integral:

[tex]\int_{\gamma} |z|^2 dz[/tex] where [tex]\gamma(t)[/tex] is the line segment from 2 to 3 + i

Homework Equations

Green's Theorem

The Attempt at a Solution

I originally started by saying that y = x - 2 and subing that into the equation "x^2 + y^2". Then tried to integrat it but failed.

Where am I going wrong?

 

[lanedance]

So
z = x+i.y

Parameterise the line by
x(t)=t
y(t)=t-2

Now write the parameterised of the line z(t), then find the differential dz in terms of dt, then perform the integration over t