Results 1 to 4 of 4

Math Help - Complex Numbers Stuff

  1. #1
    Junior Member Evales's Avatar
    Joined
    Oct 2007
    Posts
    63

    Complex Numbers Stuff

    Represent the set {z : |z - 1| = 2 and Re z less then or equal to 0} on an Argand Diagram.

    I have never come across this type of question. Any hints on how to tackle it?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Evales View Post
    Represent the set {z : |z - 1| = 2 and Re z less then or equal to 0} on an Argand Diagram.

    I have never come across this type of question. Any hints on how to tackle it?
    {z : |z - 1| = 2} ..... The distance of z from 1 is always equal to 2. Geometrically then z lies on a circle of radius 2 and centre at z = 1.

    {z : Re z less then or equal to 0} ..... You have the left half of the complex plane (the part to the left of the Im(z) axis).

    Put the two together and look for the overlap ......
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
    Posts
    591
    Quote Originally Posted by Evales View Post
    Represent the set {z : |z - 1| = 2 and Re z less then or equal to 0} on an Argand Diagram.

    I have never come across this type of question. Any hints on how to tackle it?
    This is a standard problem about loci in the complex plane. Are you familiar with the following ?

    • |z| = r describes a circle at the origin of radius r
    • |z- (a +bi)| = r describes a circle with centre (a ,b) and radius r
    •  |z - (a +bi) | = |z - (c +di) | is the perpendicular bisector of the line joining the points (a ,b) and (c ,d)


    If you know this problem should be very easy, otherwise using the information I gave you attempt the problem and let me know I you have any issues.

    Bobak
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member Evales's Avatar
    Joined
    Oct 2007
    Posts
    63
    Ahh thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex function C-R stuff
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: October 3rd 2011, 07:45 PM
  2. Replies: 1
    Last Post: September 27th 2010, 03:14 PM
  3. proving complex stuff
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 2nd 2009, 05:31 AM
  4. Complex Analysis, Plotting basic stuff
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 25th 2009, 07:13 AM
  5. Replies: 1
    Last Post: May 24th 2007, 03:49 AM

Search Tags


/mathhelpforum @mathhelpforum