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Splitting Infinite Series into Real and Imaginary Parts 
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#1
Apr812, 12:58 PM

P: 294

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
Apr812, 01:22 PM

P: 606

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 


#3
Apr812, 01:26 PM

P: 294

Ok cool, thanks.



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