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Solving complex exponential polynomials

  1. Dec 2, 2009 #1
    Are there any general methods to solve the following complex exponential polynomial without relying on numerical methods? I want to find all possible solutions, not just a single solution.

    e^(j*m*[tex]\theta1[/tex]) + e^(j*m*[tex]\theta2[/tex])+e^(j*m*[tex]\theta3[/tex]) + e^(j*m*[tex]\theta4[/tex]) + e^(j*m*[tex]\theta5[/tex]) = 0

    where

    [tex]\theta1[/tex]<[tex]\theta2[/tex]<[tex]\theta3[/tex]<[tex]\theta4[/tex]<[tex]\theta5[/tex]

    and

    m is a integer
     
  2. jcsd
  3. Dec 2, 2009 #2
    At first a question:
    Why do you include m? You could absorb it into the thetas?
    The ordering of the thetas probably doesnt play a role either.

    With that in mind you could probably solve these equations this way:
    The sum of three terms should be smaller than 2 in magnitude. Then it is always possible to find the final two exponentials.
     
    Last edited: Dec 3, 2009
  4. Dec 3, 2009 #3
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