Results 1 to 6 of 6

Math Help - Complex contour integration

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    2

    Complex contour integration

    Let \gamma be the square with vertices 0, 1, \imath+1, \imath traversed counterclockwise. Evaluate
    \int_{\gamma}{|z|^2dz}.

    I parametrized and then deduced the formula:
    \int _{\gamma }\left|z|^2dz\right.=\sum _{i=1}^4 \int _{\gamma _i}|\gamma _i(t)|^2\gamma _i'(t)dt. I come up with -1+ \imath as the answer. Please verify, thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by Eudaimonia View Post
    Let \gamma be the square with vertices 0, 1, i+1, i traversed counterclockwise. Evaluate
    \int_{\gamma}{|z|^2dz}.

    I parametrized and then deduced the formula:
    \int _{\gamma }\left|z|^2dz\right.=\sum _{i=1}^4 \int _{\gamma _i}|\gamma _i(t)|^2\gamma _i'(t)dt. I come up with -1+i as the answer. Please verify, thank you.
    I agree with your answer.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    195
    Quote Originally Posted by Opalg View Post
    I agree with your answer.
    Why wouldn't the answer be zero under Cauchy's theorem?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2010
    Posts
    2
    Please correct me if I'm wrong, but I don't think f(z)=|z|^2 is holomorphic at 0, and thus it does not meet that requirement of Cauchy's integral theorem.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Mar 2010
    From
    Beijing, China
    Posts
    293
    Thanks
    23
    because |z|^2 = zz* is not analytic
    Quote Originally Posted by davismj View Post
    Why wouldn't the answer be zero under Cauchy's theorem?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2009
    Posts
    195
    Quote Originally Posted by xxp9 View Post
    because |z|^2 = zz* is not analytic
    duh
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex Contour Integration With Branch Cut
    Posted in the Calculus Forum
    Replies: 0
    Last Post: December 8th 2010, 02:52 PM
  2. Complex Contour Integrals
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 16th 2010, 09:50 PM
  3. Complex Contour Integral
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 23rd 2010, 11:58 AM
  4. Complex Contour Integral
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 15th 2010, 07:34 PM
  5. Complex Contour Question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 25th 2009, 04:00 PM

Search Tags


/mathhelpforum @mathhelpforum