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