Results 1 to 2 of 2

Math Help - Complex analysis, Cauchy's integral theorem

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    56

    Complex analysis, Cauchy's integral theorem

    Use cauchy's integral formula to evaluate
    \oint \frac{e^{sin(z)}}{z^2(z-\frac{\pi}{4})}

    over the curve,
    c:=|z|=\frac{\pi}{8})

    Okay, so i used the method shown in lectures,

    Since the only singularity inside C is for z=0,

    we let ,

    f(z)=\frac{e^{sin(z)}}{(z-\frac{\pi}{4})}

    hence, by cauchy's formula, z=0

    (2\pi i).\frac{e^{sin(0)}}{(0-\frac{\pi}{4})}= -8i

    But the answer says -32/pi*(1+pi/4)i

    Just starting this topic, so still trying to wrap my head around it.

    Thanks in advanced
    Last edited by olski1; August 21st 2011 at 12:01 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    44

    Re: Complex analysis, Cauchy's integral theorem

    Quote Originally Posted by olski1 View Post
    Since the only singularity inside C is for z=0, we let , f(z)=\frac{e^{sin(z)}}{(z-\frac{\pi}{4})} hence, by cauchy's formula, z=0 (2\pi i).\frac{e^{sin(0)}}{(0-\frac{\pi}{4})}= -8i
    It should be 2\pi i f'(0) , not 2\pi i f(0) .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex variables(Cauchy Integral Theorem)
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: October 18th 2010, 06:04 PM
  2. Complex Analysis: Cauchy's Theorem
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 5th 2010, 02:24 AM
  3. cauchy inequalities [complex analysis]
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 15th 2010, 02:28 PM
  4. Using generalized Cauchy Theorem(complex analysis)
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 19th 2010, 08:58 AM
  5. Complex Analysis: cauchy's theorem
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: November 16th 2009, 04:05 AM

Search Tags


/mathhelpforum @mathhelpforum