1. The problem statement, all variables and given/known data show that a sequence zn (of complex numbers) converges if and only if it's real and imaginary parts converge. 2. Relevant equations 3. The attempt at a solution if the real parts converge and the imaginary parts converge then using linearity, we have: lim(real + imaginary)= lim(real) + lim(imaginary) I think this is a wrong proof (and surely incomplete). does anyone have any ideas?