Results 1 to 3 of 3

Math Help - Complex Variables

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    5

    Complex Variables

    Can anyone help me with this pls?

    How can you prove that the integral of f(z) around the contour z= 1 is 0

    where f(z) is Log(z+5)

    Thx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2008
    Posts
    5
    I know Log(z) is ln r + i (theta). But i dont know how that applies to this situation.

    Also, do I solve it as a normal integral or use the Cauchy Goursat theorem to prove that its integral is zero?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by stillsoulsearching View Post
    Can anyone help me with this pls?

    How can you prove that the integral of f(z) around the contour z= 1 is 0

    where f(z) is Log(z+5)

    Thx
    Because \log (z+5) is analytic on \mathbb{C} - (\infty,-5]. This is a simply connected domain and Cauchy's theorem tells us that the integral over a (rectifiable) curve of an analytic function on a simply connected domain is zero.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex Variables
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: February 5th 2010, 05:12 AM
  2. help with complex variables
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: February 5th 2010, 05:12 AM
  3. complex variables
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 28th 2010, 01:28 PM
  4. Complex Variables
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 13th 2009, 08:27 PM
  5. complex variables
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 28th 2008, 05:21 AM

Search Tags


/mathhelpforum @mathhelpforum