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Sequences in complex (just a clarifying question)

  • Thread starter bennyska
  • Start date
  • #1
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Homework Statement


(excuse lack of latex)
show that if SUM(zn)= S and SUM(wn= T, then SUM(zn + wn) = S + T


Homework Equations





The Attempt at a Solution



so if i'm doing this right, this is pretty easy, i think. they want me to use a theorem that says if zn=xn +iyn, and SUM(zn)= S, where S = X + iY, this happens iff SUM(xn)= X and SUM(yn)= Y.

so my question is am i allowed to say SUM(zn + wn) = SUM(zn) + SUM(wn) = SUM(xn) + iSUM(yn) + SUM(un) + iSUM(vn)? i'm not sure if i'm violating anything by breaking it up like this. it all follows very quickly from here.

*edit: forgot to erase double standard questions after preview
 

Answers and Replies

  • #2
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
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You can break it up as:
SUM(xn+un)+iSUM(yn+vn)

just using the property that you posted (make sure you understand why). To go further you need to do something else
 

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