|Apr8-12, 12:58 PM||#1|
Splitting Infinite Series into Real and Imaginary Parts
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]
|Apr8-12, 01:22 PM||#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.
|Apr8-12, 01:26 PM||#3|
Ok cool, thanks.
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