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

Math Help - Complex analysis r-neighbourhood problem

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    London
    Posts
    3

    Complex analysis r-neighbourhood problem

    hi, i need some help with the following problem:

    Let

    z = a + ib , w = x + iy be two complex numbers that belong tothe neighbourhoodN(0, r).

    Show that at least one of
    a + iy; x + ib also lies in N(0, r).

    i'm not sure where to begin with solving this problem, any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,403
    Thanks
    1486
    Awards
    1

    Re: Complex analysis r-neighbourhood problem

    Quote Originally Posted by paulluap1991 View Post
    Let
    [LEFT][B]
    z = a + ib , w = x + iy be two complex numbers that belong tothe neighbourhoodN(0, r).

    Show that at least one of
    a + iy; x + ib also lies in N(0, r[FONT=CMR12]).
    From the given you know that a^2+b^2<r^2\text{ and }x^2+y^2<r^2.

    Now you want to show that a^2+y^2<r^2\text{ OR }x^2+b^2<r^2.

    Suppose that a^2+y^2\ge r^2\text{ and }x^2+b^2\ge r^2.
    Thanks from paulluap1991
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,988
    Thanks
    1128

    Re: Complex analysis r-neighbourhood problem

    I would start by drawing a circle, representing the neighborhood, in the complex plane and look at pairs of points. Given points (a, b) and (x, y) the points (a, y) and (x, b) together with them form a rectangle. Can you find points (a, b) and (x, y) so that not both (a, y) and (x, b) are in N?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. a problem about complex analysis
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: May 4th 2012, 01:34 PM
  2. A problem in complex analysis
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: April 13th 2012, 05:08 PM
  3. Neighbourhood of an irrational
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 12th 2011, 09:11 AM
  4. Another complex analysis problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 13th 2008, 07:28 AM
  5. One More Complex Analysis Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 19th 2006, 12:54 AM

Search Tags


/mathhelpforum @mathhelpforum