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Tau and phi (conjugates?) fibonacci sequence

  1. Jul 3, 2011 #1
    1. The problem statement, all variables and given/known data
    Would tau and phi be considered conjugates?

    2. Relevant equations
    [itex]\tau[/itex] = [itex]\frac{1-\sqrt{5}}{2}[/itex]
    [itex]\phi[/itex] = [itex]\frac{1+\sqrt{5}}{2}[/itex]

    3. The attempt at a solution
    I know that a complex number such as 1+2i would have 1-2i as a conjugate. However, for fractions, I can't quite remember if the same rule applies.

    Thank you in advance
  2. jcsd
  3. Jul 4, 2011 #2


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    Homework Helper

    yes, the reason is tau x phi will give a results with not square roots in the expression

    similarly for complex numbers, the result of multiplying conjugates is real
  4. Jul 4, 2011 #3
    Thank you! This will help me better understand the binet formula :biggrin:
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