Results 1 to 3 of 3

Math Help - Simple intro to complex variables question

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    168

    Simple intro to complex variables question

    I have to show that
    |(2\overline{z}+5)(\sqrt{2}-i)|=\sqrt{3}|2z+5|

    So far, I have
    |(2\overline{z}+5)(\sqrt{2}-i)|=|2\overline{z}+5||\sqrt{2}-i)|

    My sol'n book then says this is equal to
    |\overline{2z+5}|\sqrt{2+1}

    I understand that for the second term they are just finding the length, but I don't understand how
    |2\overline{z}+5|=|\overline{2z+5}|.

    Can anyone explain the math behind that?
    Last edited by paupsers; January 12th 2010 at 06:53 AM. Reason: PS: Also, is this the right forum to post questions about complex variables?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301
    Quote Originally Posted by paupsers View Post
    I have to show that
    |(2\overline{z}+5)(\sqrt{2}-i)|=\sqrt{3}|2z+5|

    So far, I have
    |(2\overline{z}+5)(\sqrt{2}-i)|=|2\overline{z}+5||\sqrt{2}-i)|

    My sol'n book then says this is equal to
    |\overline{2z+5}|\sqrt{2+1}

    I understand that for the second term they are just finding the length, but I don't understand how
    |2\overline{z}+5|=|\overline{2z+5}|.

    Can anyone explain the math behind that?
    Suppose  z = a+bi . Then  \overline{z} = a-bi . So  \overline{2} = 2 and  \overline{5} = 5 .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,648
    Thanks
    1596
    Awards
    1
    Here is a bit more.
    Notice that \sqrt {\left( x \right)^2  + \left( y \right)^2 }  = \sqrt {\left( x \right)^2  + \left( { - y} \right)^2 } . So that means that \left| z \right| = \left| {\overline z } \right|.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another complex variables question.
    Posted in the Calculus Forum
    Replies: 0
    Last Post: August 31st 2010, 06:28 AM
  2. quick question complex variables
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 29th 2010, 02:19 PM
  3. Simple complex number question
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 20th 2010, 07:23 AM
  4. Simple complex analysis question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 31st 2009, 04:22 PM
  5. simple complex conjugates question
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 17th 2008, 10:22 PM

Search Tags


/mathhelpforum @mathhelpforum