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Can magnitude of complex numbers raised to some power

  1. Sep 1, 2011 #1
    Hey People just a general question

    Is the following necessarily possible?

    |z23|=|z|23

    Where z is a complex number. I can't think of a reason why not but then again complex numbers have some subtle behaviours.

    Thanks
     
  2. jcsd
  3. Sep 1, 2011 #2

    Hootenanny

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    Welcome to Physics Forums.
    If we take a look in polar form, we have

    [tex]|z^{n}| = ||z|^ne^{in\cdot\text{arg}z}| = |z|^n|e^{in\cdot\text{arg}z}| = |z|^n[/tex]
     
  4. Sep 1, 2011 #3
    Haha I can't believe I didn't try polar form. Thanks for that
     
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