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

Splitting Infinite Series into Real and Imaginary Parts

  1. Apr 8, 2012 #1
    I need a quick reminder that this is (hopefully) true:

    Let [itex]\sum a_n[/itex] be an infinite series of complex terms which converges but not absolutely. Then can we still break it up into its real and imaginary parts?

    [tex]\sum a_n = \sum x_n + i\sum y_n[/tex]
     
  2. jcsd
  3. Apr 8, 2012 #2


    Well, since a (complex, real or whatever, as long as we have a definite meaning for infinite sums) series converges iff the sequence of its partial sums converges finitely, and a complex seq. converges iff its real and imaginary parts converge, then...yes.

    DonAntonio
     
  4. Apr 8, 2012 #3
    Ok cool, thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Splitting Infinite Series into Real and Imaginary Parts
Loading...