$ \fcolorbox{white}{yellow}{$\sum_{n=1}^\infty z_n
= \sum_{n=1}^\infty x_n +i \sum_{n=1}^\infty y_n $ if both $\sum_{n=1}^\infty x_n$ and
$\sum_{n=1}^\infty y_n$ are convergent.}$
$\sum_{n=1}^\infty |z_n|$ converges if and only if both $\sum_{n=1}^\infty x_n$ and
$\sum_{n=1}^\infty y_n$ are convergent absolutly.
$ \fcolorbox{white}{yellow}{All tests in Chapter 1 applies to the case of absolute convergence}$.
Complex power series $\sum_{n=0}^\infty a_n z^n$.
Disk of convergence $|z|< R$.
$\frac1R = \lim_{n\to\infty} \frac{|a_{n+1}|}{|a_n|} \fcolorbox{white}{yellow}{Caution: the formula fails if the limit does not exist}$