Results 1 to 2 of 2

Math Help - Q [sq rt 3 +i] is a unit

  1. #1
    Junior Member
    Joined
    Mar 2007
    Posts
    40

    Q [sq rt 3 +i] is a unit

    Problem: Every nonzero element of Q [sq rt 3 + i] is a unit. Prove answer?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by chadlyter View Post
    Problem: Every nonzero element of Q [sq rt 3 + i] is a unit. Prove answer?
    Since
    sqrt(3)+i
    Is algebraic over Q.
    Because it is a zero of,
    x^4 - 2x^2-8

    It means that,
    Q[sqrt(3)+i]
    Simple field extension over Q.

    Thus, it is a field and hence, all non-zero elements are units.

    This is Mine 52th Post!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. unit length unit rise ratio
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: October 16th 2011, 08:45 PM
  2. Unit
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: February 17th 2011, 05:22 PM
  3. Replies: 0
    Last Post: February 8th 2011, 10:54 AM
  4. unit of integration vs unit of boundaries
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 12th 2009, 09:14 PM
  5. Replies: 3
    Last Post: September 17th 2009, 07:35 PM

Search Tags


/mathhelpforum @mathhelpforum