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I Parametric Resonance

  1. Mar 11, 2017 #1
    pf.png
    Why ##\mu_1, \mu_2## must be the same as ##\mu_1^*, \mu_2^*## ?

    What I thought is : If ##\mu_1\mu_2 = \mu_1^*\mu_2^*## and ##\mu_1+\mu_2 = \mu_1^*+\mu_2^*##, then ##\mu_1, \mu_2## are the same as ##\mu_1^*, \mu_2^*##

    It can be shown by taking the complex conjugate of (27.5) that $$\mu_1\mu_2 = \mu_1^*\mu_2^*=1$$
    Now it is to be proven that ##\mu_1+\mu_2 = \mu_1^*+\mu_2^*##.
    Any help would be appreciated.
     
    Last edited: Mar 11, 2017
  2. jcsd
  3. Mar 11, 2017 #2

    scottdave

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    If u1 = (a + bi) and u2 = (c + di), then you can write (a + bi)(c + di) = 1. Expanding it, you get:

    ac + adi + bci – bd = 1. Rearrange as (ac – bd) + i(ad + bc) = 1. So (ac – bd) = 1, and (ad + bc) = 0. You may be able to get a starting point from that. If possible, I will try to come back and revisit this.
     
  4. Mar 12, 2017 #3
    Thanks for your help. But still could not get it.
     
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