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: Order of poles

  1. Mar 27, 2006 #1
    I'm having trouble determining the order of the pole of

    [exp(iz) - 1]/((z^2) + 4) at z=2i

    I know I can't just expand the exponential as 1 + iz + [(iz)^2]/2 .......
    because this formula only works near the origin. Can I still use Taylor's theorem to find the expansion at z=2i (i.e does Taylor's theorem still work for complex variables?)
    thanks for your help.
  2. jcsd
  3. Mar 27, 2006 #2


    User Avatar
    Science Advisor

    It's pretty obvious, isn't it, that f(z)(z-2i)= (eiz-1)/(z+2i) is analytic at z= 2i while f(z) itself is not. z= 2i is a pole of order 1.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook