- #1

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## Homework Statement

(excuse lack of latex)

show that if SUM(z

_{n})= S and SUM(w

_{n}= T, then SUM(z

_{n}+ w

_{n}) = 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 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