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Interpret the angle of the complex number

  1. Jan 15, 2012 #1
    Hi,

    1. The problem statement, all variables and given/known data
    Interpret the angle of the complex number [itex](z_{1} - z_{2}) / (z_{1} - z_{3})[/itex]
    in the triangle formed by the points [itex]z_{1}, z_{2}, z_{3}[/itex].

    2. Relevant equations



    3. The attempt at a solution
    I'm not entirely sure what to do in this question, I've done a couple of examples with some complex numbers but haven't noticed anything special about the resulting angle. I'm also a bit confused by what 'Interpret' means. Any help with this will be greatly appreciated.

    thanks!
    babak
     
  2. jcsd
  3. Jan 15, 2012 #2

    SammyS

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    In the examples you tried, how does the angle formed at the z1 compare with the argument of [itex]\displaystyle\frac{z_{1} - z_{2}}{z_{1} - z_{3}}\,?[/itex]
     
  4. Jan 16, 2012 #3
    I've seen this question before
    if you think about z1-z2, that's just like a vector from z1 to z2, yes

    so try and relate the division of the angles to the dot products of normal vectors
     
  5. Jan 22, 2012 #4
    Hi guys,

    Thanks for the responses, I think I see now. So the angle formed at [itex]z_{1}[/itex] is the same as the argument of [itex]\frac{z_{1} - z_{2}}{z_{1} - z_{3}}[/itex] ?

    thanks
    babak
     
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