(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(excuse lack of latex)

show that if SUM(z_{n})= S and SUM(w_{n}= T, then SUM(z_{n}+ w_{n}) = S + T

2. Relevant equations

3. 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 z_{n}=x_{n}+iy_{n}, and SUM(z_{n})= S, where S = X + iY, this happens iff SUM(x_{n})= X and SUM(y_{n})= Y.

so my question is am i allowed to say SUM(z_{n}+ w_{n}) = SUM(z_{n}) + SUM(w_{n}) = SUM(x_{n}) + iSUM(y_{n}) + SUM(u_{n}) + iSUM(v_{n})? 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

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# Homework Help: Sequences in complex (just a clarifying question)

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