Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Rebesques

Math Help - Complex Analysis - f is holomorphic...

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    20

    Complex Analysis - f is holomorphic...

    Hey guys. Heres my problem:

    f is holomorphic on C and of the form f(x + iy) = u(x) + i v(y) where u and v are real functions, then f(x) = \lambda z + c with \lambda \in R and c \in C.

    Where C is the coplex numbers and R is the real numbers.

    Earlier I've made an assignment where I show that if f is holomorphic in a domain G and |f| is constant, then f is constant. So I'm guessing I have to show that f' is constant, which then tells me that there exists some \lambda so f(z) = \lambda z + c, but I dont know how to do that.

    If anyone could assist I would greatly appreciate it.

    /Morten
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Rebesques's Avatar
    Joined
    Jul 2005
    From
    At my house.
    Posts
    538
    Thanks
    11

    Re: Complex Analysis - f is holomorphic...

    Use the Cauchy-Riemann equations to show that u' and v' are constant.
    Thanks from Deveno
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2011
    Posts
    20

    Re: Complex Analysis - f is holomorphic...

    Ah of course

    Thanks for the help.

    /Morten
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: September 13th 2011, 07:16 AM
  2. Is the conjugate of a complex function holomorphic?
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: November 19th 2010, 03:19 AM
  3. Replies: 0
    Last Post: October 17th 2010, 04:52 PM
  4. Complex differentiable and holomorphic functions
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: December 7th 2009, 04:03 PM
  5. Replies: 1
    Last Post: March 3rd 2008, 07:17 AM

Search Tags


/mathhelpforum @mathhelpforum