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Complex numbers

  1. Nov 29, 2011 #1
    How does one prove that for w≠+-1 , w a complex number, there are exactly 2 solutions to the equation w=0.5(z+1/z)? i'm at a total loss here. Could someone clue me in on this one?
     
  2. jcsd
  3. Nov 29, 2011 #2
    What if you multiplied each side by 2z?
     
    Last edited: Nov 29, 2011
  4. Nov 30, 2011 #3

    HallsofIvy

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    The best way to prove there are two solutions is to find them! That is what ramsey2879 is suggesting.
     
  5. Nov 30, 2011 #4
    I do believe that the quadratic formula will work for equations with complex coefficients even if it is not clear (at least to me) how to find the square root of a complex number. Just write the solution out in the radical form simplified as far as posible.
     
  6. Dec 1, 2011 #5
    Do a internet search: complex numbers solve square root
     
  7. Dec 2, 2011 #6
    w=0.5(z+1/z)
    w=0.5z+0.5/z
    wz=0.5z^2+0.5
    0.5z^2+0.5-wz=0

    If you could substitute a value of either w or z you could work out the other using Quadratic Formula

    x = (-b +- sqrt(b^2-4ac))/2a

    Other than this, I can't see how you solve it since you have 2 unknowns. Either way you have a squared value for z so z has 2 solutions.

    Sorry if I was no help, this is my first post here as I just joined today. :)
     
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