Decide whether each of the following sequences converges, and if so, type the limit in the answer blank.

If it does not converge, type $DNC$ :

(1) $z_n\ =\ \frac{i}{n}$

(2) $z_n\ =\ i(-1)^n$

(3) $z_n\ =\ Arg(-1\ +\ \frac{i}{n})$

(4) $z_n\ =\ \frac{n(2\ +\ 4 i)}{n\ +\ 1}$

(5) $z_n\ =\ (\frac{1\ -\ i}{4})^n$

(6) $z_n\ =\ exp(\frac{2n\pi i}{5})$