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Complex Line Integrals

  • Thread starter loki91
  • Start date
  • #1
3
0

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?
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
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
 

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