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Finding length of a complex number

  1. Jan 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    Please take a look at this complex number:

    [tex]
    \widehat C = \frac{1-\widehat a}{1+\widehat a}\widehat B,
    [/tex]

    where a hat indicates that the number is complex. Can you confirm me in that the length (modulus) of this complex number [itex]|\widehat C|[/itex] is given by:

    [tex]
    |\widehat C| = \frac{|1-\widehat a|}{|1+\widehat a|}|\widehat B|
    [/tex]

    Thanks in advance.

    Best regards,
    Niles.
     
  2. jcsd
  3. Jan 6, 2009 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes, but you need to be careful. Note that if [itex]\widehat{a} = \alpha + i\beta[/itex] then

    [tex]\left|1-\widehat{a}\right| = \sqrt{\left(1-\alpha\right)^2 + \beta^2}[/tex]
     
  4. Jan 6, 2009 #3
    Thanks a lot for responding quickly.
     
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