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Homework Help: U(dot)U != ||U||^2 help?

  1. Mar 31, 2009 #1
    1. The problem statement, all variables and given/known data

    well i am told basicly this
    |u|^2 = U dot U except when in using imaginary numbers
    i tried using the example below and a few others but it seems to always work for me :/
    but i need the process or to show this is not true

    2. Relevant equations

    ||u|| = U dot U in general not complex :/

    3. The attempt at a solution

    2i + 5
     
  2. jcsd
  3. Apr 1, 2009 #2

    CompuChip

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    Science Advisor
    Homework Helper

    What are u and U?
    Are they the same (U = u)?
    Is u a vector, of which |u| is the norm, or just a number of which |u| is the absolute value (for real numbers) or the modulus (for complex ones). Or is it a matrix, for which |u| is some matrix norm?

    If it is a number, it's rather easy to show.
    The modulus (length) of 2i + 5 is [itex]\sqrt{2^2 + 5^2}[/itex] which is not equal to (2i + 5)^2.

    In general, the correct expression is
    |u|^2 = u . u*
    where u* is the complex conjugate of u.
     
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