Results 1 to 2 of 2

Thread: [SOLVED] Complex Analysis Proof

  1. February 5th 2009, 06:50 PM #1
    ronaldo_07
    ronaldo_07 is offline
    Member ronaldo_07's Avatar
    Joined
    Nov 2008
    Posts
    175

    [SOLVED] Complex Analysis Proof



    How would I prove this?
    Follow Math Help Forum on Facebook and Google+
  2. February 6th 2009, 09:28 AM #2
    ThePerfectHacker
    ThePerfectHacker is offline
    Global Moderator ThePerfectHacker's Avatar
    Joined
    Nov 2005
    From
    New York City
    Posts
    10,603
    Write f(x+iy) = u(x,y) + iv(x,y).
    We know that v(x,y)=0 by hypothesis.
    But, u_x = v_y \implies u_x = 0 \implies u(x,y) = g(y).
    And, u_y = -v_x \implies u_y = 0 \implies u(x,y) = h(x).
    Therefore, g,h need to be constant functions.
    And so u(x,y) = c.
    Follow Math Help Forum on Facebook and Google+
« Finding Tangent Lines | [SOLVED] derivatives »

Similar Math Help Forum Discussions

  1. Complex Analysis: Proof that a straight line in Complex Plane is a connected set
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: September 13th 2011, 07:16 AM
  2. [SOLVED] Complex analysis, determine the set in the complex plane that satisfies...
    Posted in the Differential Geometry Forum
    Replies: 12
    Last Post: June 2nd 2010, 02:30 PM
  3. Solved Complex Analysis
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 9th 2010, 12:24 PM
  4. [SOLVED] Complex Analysis
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 29th 2009, 08:27 PM
  5. [SOLVED] complex analysis help...
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 28th 2009, 03:52 PM

Search Tags


/mathhelpforum @mathhelpforum