Results 1 to 3 of 3

Math Help - complex number

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    23

    complex number

    A and B are the points representing the complex numbers z and (1 + i )z in an Argand diagram. Prove that triangle OAB is a right-angled isoceles triangle, where O is the origin.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: complex number

    Hints: |OA|=|z|,\;|OB|=\sqrt{2}|z| . On the other hand |AB|=|(1+i)z-z|=|iz|=|z| and 1+i=\sqrt{2}e^{\pi i/4} .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member kalyanram's Avatar
    Joined
    Jun 2008
    From
    Bangalore, India
    Posts
    143
    Thanks
    14

    Re: complex number

    Given:
    OA = z, OB = (1 + i)z
    By the definition of multiplication of complex numbers if z_1 = r_1. cis {\theta}_1, z_1 = r_2. cis {\theta}_2 we have
    z_1.z_2 = r_1.r_2 cis({\theta}_1 + {\theta}_2) so we have z_1 = (1 + i) =  \sqrt 2 .cis {\frac{\pi}{4}}.
     \therefore in \Delta OAB, |OB| = \sqrt 2.|OA|, \; \angle AOB = \frac{\pi}{4}

     \therefore \Delta OAB is right isosceles triangle.

    Kalyan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 2nd 2010, 01:54 PM
  2. Replies: 3
    Last Post: September 13th 2010, 11:13 AM
  3. Sin of Complex Number
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 31st 2009, 05:40 PM
  4. Complex number
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: August 14th 2009, 05:56 AM
  5. Complex number help??
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 22nd 2008, 02:23 AM

Search Tags


/mathhelpforum @mathhelpforum