Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

From Euler's identity: i^i=exp(-pi/2)= 0.2079 (rounded)

  1. Jun 11, 2009 #1
    From Euler's identity: i^i=exp(-pi/2)= 0.2079 (rounded). I've always thought of this as an interesting result although I don't know of any particular significance or consequence of it. Is there any?
     
  2. jcsd
  3. Jun 11, 2009 #2

    disregardthat

    User Avatar
    Science Advisor

    Re: i^i

    i^i does not have a specific value. [tex]i^i=e^{i^2(\frac{\pi}{2}+2\pi \cdot n) }=e^{-(\frac{\pi}{2}+2\pi \cdot n) }[/tex] for all integers n.
     
    Last edited: Jun 12, 2009
  4. Jun 11, 2009 #3
    Re: i^i

    I'm using ^ as raising to a power except for 'exp' where exp(x) means e^x

    exp(i pi)= -1

    SQRT [exp(i pi) = SQRT (-1)

    exp(i pi/2) = i

    exp ((i^2) pi/2)) = i^i = exp (-pi/2) = 0.2079 (rounded)
     
    Last edited: Jun 11, 2009
  5. Jun 11, 2009 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Re: i^i

    SW VandeCarr:

    Jarle is also using it in that sense.

    However, as he pointed out, the complex logarithm is a multi-valued mapping, in contrast to the real logarithm.
     
  6. Jun 11, 2009 #5
    Re: i^i

    Thanks, but the algebra is correct, is it not? Normally I don't see the +2pi.n term in texts.
     
    Last edited: Jun 11, 2009
  7. Jun 11, 2009 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: i^i

    Strange, I do!
     
  8. Jun 11, 2009 #7
    Re: i^i

    SW VandeCarr - you can put "tex" tags around your equations and use latex syntax instead of defining all of your notation. It makes yours and everyone else's life easier :)
     
  9. Jun 11, 2009 #8
    Re: i^i

    Thanks daviddoria. I guess it's about time I started using latex if I'm going to be posting questions here.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: From Euler's identity: i^i=exp(-pi/2)= 0.2079 (rounded)
  1. Euler's identity (Replies: 7)

Loading...