Convergence of z_n: A Complex Series Question with Alpha Boundaries

[lom]

$$z_n=\rho_ne^{i\theta_n}\\$$ is a series of complex numbers which differs 0 for which

$$-\alpha<=\theta_n<=\alpha\\$$



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



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

 

[Mark44]

What have you tried? Do you know any theorems for determining whether an infinite series converges?