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Number of complex roots

  1. Sep 8, 2010 #1
    How many complex roots admit the following equation:
    (2 z^2 + 1)^2 ((z + d)/(z - i))^1/2 - (2 z^2 - d)^2 ((z + i)/(z - d))^1/2 == 0
    for 0 < d < 1, where i = (-1)^1/2.
    Can I found how their number varies with d by using the argument principle?
    Thanks in advance for helpfull suggestions
  2. jcsd
  3. Sep 9, 2010 #2
    You get a fourth deg. equation in z^2 equation on simplification, so a maximum of 8 zeroes is possible.
  4. Sep 9, 2010 #3
    Yes, but which of them are actually zeroes of the starting equation?
    Thanks for your intrest
  5. Sep 9, 2010 #4
    I found numerically that for small d only four roots are admissible (two reals and two purely imaginary) but for large d two more complex conjugate roots appear.
    There exists any analitical tools to define this critical value of d?
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