Results 1 to 5 of 5

Math Help - How do you algebraically manipulate absolute valued variables?

  1. #1
    Junior Member
    Joined
    Dec 2009
    Posts
    69
    Thanks
    1

    How do you algebraically manipulate absolute valued variables?

    For example: 2x^2-|x|^2 and 2y^2-|y|^2 in the attached img. Does 2x^2-|x|^2 equal x^2 or |x|^2 or both?

    Is there a difference between |x|^2 and x^2?

    It seems the first term refers to the square of the magnitude and the second of whatever happens to be the domain.
    Attached Thumbnails Attached Thumbnails How do you algebraically manipulate absolute valued variables?-untitled.png  
    Last edited by Elusive1324; August 12th 2013 at 06:04 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,612
    Thanks
    591

    Re: How do you algebraically manipulate absolute valued variables?

    Hey Elusive1324.

    There is no difference between |x|^2 and x^2 in terms of the map. In other words for the same values of x you get the same y for both functions. If you really want to prove it then break up the |x| into negative and positive x and show that the relationship holds since you get analytic functions (-x for x < 0 and x for x >= 0) which can be compared.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    828
    Thanks
    209

    Re: How do you algebraically manipulate absolute valued variables?

    in fact when we talk of square it does not make a difference. in that case x^2 = ( |x| )^2
    As we know the modulus function is defined as
    |x| = -x for x < 0 and |x| = x for x = > 0.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Dec 2009
    Posts
    69
    Thanks
    1

    Re: How do you algebraically manipulate absolute valued variables?

    If the mapping is the same, then what is the point of writing it as |x|^2 in the steps?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1

    Re: How do you algebraically manipulate absolute valued variables?

    Quote Originally Posted by Elusive1324 View Post
    If the mapping is the same, then what is the point of writing it as |x|^2 in the steps?
    Let's just prove this. It has been several days now.

    For all real numbers a~\&~b it is true that a^2+b^2\ge 2|ab|

    Suppose that z=x+yi, so
    \\x^2+y^2\ge 2|xy|\\2x^2+2y^2\ge x^2+ 2|xy|+y^2\\2|z|^2\ge (|x|+|y|)^2

    Thus \sqrt2|z|\ge|\text{Re}(z)|+|\text{Im}(z)|~.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to rearrange/manipulate algebraically?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 17th 2012, 05:39 PM
  2. Replies: 1
    Last Post: December 6th 2011, 11:47 AM
  3. Replies: 0
    Last Post: December 6th 2010, 04:44 AM
  4. Absolute Extrema (two variables)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 13th 2009, 12:24 PM
  5. Extrema (Absolute) - Two variables
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 15th 2007, 07:22 PM

Search Tags


/mathhelpforum @mathhelpforum