1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Taylor series for i^i?

  1. Oct 27, 2003 #1
    I'm having some problems expanding i^i, could anyone help? I know it becomes a real number somehow, and I'm familiar with the e^(i * pi) expansion, but is the i^i done in the same way?
  2. jcsd
  3. Oct 27, 2003 #2


    User Avatar
    Science Advisor

    There is a well known expansion for a^x:


    Just replace a and x with i.

    At first glance, it doesn't look real to me, but maybe the sum telescopes.

  4. Oct 27, 2003 #3
    Hello, Khan!

    I'm not sure what you mean by expanding ii,
    since it is already a constant.

    Using DeMoivre's Theorem (Euler's?): eix = cos x + i sin x,
    when x = pi/2, we have: ei*pi/2 = cos(pi/2) + i sin(pi/2) = i

    Raise both sides to the power i: ii = (ei*pi/2)i= e-pi/2 = 0.207879576...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook