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Help with natural logs

  1. Apr 9, 2004 #1
    what is the result or simplification of

    ( ln(i^2) )^2

    sweet bro
    :confused:
     
  2. jcsd
  3. Apr 9, 2004 #2

    Janitor

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    Easy as pi

    First, i^2=-1.

    Then note that exp(i pi) = -1.

    So ln(-1) = ln[exp(i pi)] = i pi.

    Square it: (i pi)^2 = - pi^2.

    EDIT: I should caution that this is a solution. I make no claim that it is the only solution.
     
    Last edited: Apr 9, 2004
  4. Apr 9, 2004 #3

    chroot

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    [itex]-\pi^2[/itex] is definitely a solution. I'm not sure how there could be more solutions...?

    - Warren
     
  5. Apr 9, 2004 #4
    He wasn't even referring to solutions, was he? He just wanted a simplification of an expression, no?

    cookiemonster
     
  6. Apr 9, 2004 #5

    chroot

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    Well, heh, right, not solutions... I meant that [itex]-\pi^2[/itex] is the simplest possible form for it. I see what Janitor was saying now -- that there may be better simplifications. If so, I don't see any.

    - Warren
     
  7. Apr 9, 2004 #6

    Janitor

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    Cookiemonster: he did ask, "What is the result..."

    Chroot, here's the sort of thing I am worried about:

    Note that exp(3 i pi) = -1.

    So ln(-1) = ln[exp(3 i pi)] = 3 i pi.

    Square it: (3 i pi)^2 = - 9 pi^2.
     
  8. Apr 9, 2004 #7

    matt grime

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    the principal branch is usually what we mean when we ask for log of a complex number, which is the same as the principal value of arg, ie Arg
     
  9. Apr 10, 2004 #8
    thanks for all ur help dudes, and yea I believe this is a solution aswell as a simplification.
     
  10. Apr 10, 2004 #9

    Hurkyl

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    When I took complex analysis, we used ln for the multivalued version and Ln for the principal branch.
     
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