Results 1 to 2 of 2

Math Help - some algebra with complex numbers

  1. #1
    Ant
    Ant is offline
    Member
    Joined
    Apr 2008
    Posts
    137
    Thanks
    4

    some algebra with complex numbers

    Let c,a \in \mathbb{C} be constants, let n,m \in \mathbb{N}, and let z be a complex variable.

    Is it true that:

     \bigl(c(|z|+1)^n +|a| \bigr) \ |z|^m = c_0 (|z|+1)^{n-m}

    For a suitable constant c_0?

    It would be very helpful if this were true for a proof I'm trying to figure out...

    Thanks
    Last edited by Ant; April 21st 2013 at 04:26 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2010
    Posts
    909
    Thanks
    205

    Re: some algebra with complex numbers

    It doesn't seem like it would be possible - if |z| is large, the left-hand side grows like |z|^{n+m} and the right-hand side grows like |z|^{n-m}.

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Algebra with complex numbers!
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 29th 2012, 02:32 PM
  2. Algebra of complex numbers - a few questions
    Posted in the Algebra Forum
    Replies: 6
    Last Post: April 27th 2009, 08:28 PM
  3. Algebra 2 - Complex Numbers
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 27th 2008, 10:18 AM
  4. Replies: 4
    Last Post: November 11th 2008, 03:53 PM
  5. Replies: 1
    Last Post: May 24th 2007, 03:49 AM

Search Tags


/mathhelpforum @mathhelpforum