$\displaystyle 0<\alpha<\frac{\pi}{2}\\$
$\displaystyle z_n=\rho_ne^{i\theta_n}\\$ is a series of complex numbers which differs 0 for which
$\displaystyle -\alpha<=\theta_n<=\alpha\\$

A.does $\displaystyle \sum z_n\\$ converge

B.does $\displaystyle \sum |z_n|\\$ converge