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B Implications of e^i*pi = -1

  1. Aug 17, 2016 #1
    Before I start, there are only really two pieces of information this concerns and that is the idea that 1x = 1 and that ei*π = -1

    So it would follow that (ei*π)i = -1i
    And so that would mean that i2i = e which doesn't seem to be right at all. Where is the issue here as there must be one but I am sure I don't have the knowledge required to figure it out.
     
  2. jcsd
  3. Aug 17, 2016 #2

    Bystander

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    Re-investigate this aspect.
     
  4. Aug 17, 2016 #3
    I've edited it to make another point anyway hahaha but yeah I shall
     
  5. Aug 17, 2016 #4

    Bystander

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    Point of order: please do NOT make changes to your original post. It makes very confusing reading for late arriving participants.
     
  6. Aug 17, 2016 #5
    My humbumblest apologies and it shan't happen again.
     
  7. Aug 17, 2016 #6

    fresh_42

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  8. Aug 17, 2016 #7

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    De nada. You're new to the forum.
     
  9. Aug 17, 2016 #8

    mfb

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    Not all exponentiation laws work with complex numbers, and with a complex base those exponents are not unique any more.

    $$i^{2i} = e^{2i \log(i)} = e^{2i (i \pi/2)} = e^{- \pi}$$ using the principal value of the logarithm, indeed.
     
  10. Aug 17, 2016 #9
  11. Aug 17, 2016 #10
    I just find it amusing that what appears to be an extremely non real value seems to equal a simple real number
     
  12. Aug 17, 2016 #11
    I assume your log refers to ln? Sorry just being picky
     
  13. Aug 17, 2016 #12

    micromass

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    Outside of high school, logarithms with base ##e## are always denoted as ##\log##. The notation ln is not really used anymore.
     
  14. Aug 17, 2016 #13

    Mark44

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    I don't believe that's true. Every calculus textbook I have distinguishes between log (meaning base-10 logarithm) and ln. Granted, all of my textbooks are at least 15 to 20 years, and some are older.
     
  15. Aug 21, 2016 #14
    I know it adds little to the conversation, but I have to concur. Pretty much all my textbooks use ln. Maybe it's an undergrad thing?
     
  16. Aug 22, 2016 #15
    What seems to be the problem? I don't see one.
     
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