Results 1 to 5 of 5

Math Help - Sketching complex plane

  1. #1
    Member
    Joined
    Apr 2010
    Posts
    156

    Sketching complex plane

    Sketch the subset of the complex plane:

    {z E C: |z - 1| = |z - i| }

    I have no idea what to do. Could someone please explain?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by SyNtHeSiS View Post
    Sketch the subset of the complex plane:

    {z E C: |z - 1| = |z - i| }

    I have no idea what to do. Could someone please explain?
    The modulus of a complex number is it's distance from the origin in the complex plane.
    Pythagoras' theorem calculates the distance.

    z=x+iy

    z-1=(x-1)+iy\Rightarrow\ |z-1|=\sqrt{(x-1)^2+y^2}=\sqrt{x^2+y^2-2x+1}

    z-i=x+i(y-1)\Rightarrow\ |z-i|=\sqrt{x^2+(y-1)^2}=\sqrt{x^2+y^2-2y+1}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,707
    Thanks
    627
    Hello, SyNtHeSiS!

    Did you make a sketch?


    Sketch the subset of the complex plane: . \{\,z \in C\!:\;|z - 1| \:=\:|z - i|\,\}

    Hint:

    On the Argand diagram:

    . . |z-1| is the distance from \,z to (1,0).

    . . |z - i| is the distance from \,z to (0,1).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Apr 2010
    Posts
    156
    Thanks. Would this sketch be the graph y = x?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Yes, it is.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sketching regions in the complex plane
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 20th 2011, 06:33 PM
  2. Sketching Regions in the Complex Plane
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 23rd 2011, 03:22 AM
  3. Sketching regions in complex plane
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 9th 2010, 10:30 AM
  4. Sketching |z - 1| + |z + i| <= 2 in complex plane
    Posted in the Pre-Calculus Forum
    Replies: 11
    Last Post: October 28th 2010, 05:08 AM
  5. Sketching in the complex plane
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 9th 2009, 04:54 AM

Search Tags


/mathhelpforum @mathhelpforum