For each natural number $k$, choose a complex number $z _ { k }$ with $\left| z _ { k } \right| = 1$ and denote by $a _ { k }$ the area of the triangle formed by $z _ { k } , i z _ { k } , z _ { k } + i z _ { k }$. Then, which of the following is true for the series below?
$$\sum _ { k = 1 } ^ { \infty } \left( a _ { k } \right) ^ { k }$$
(A) It converges only if every $z _ { k }$ lies in the same quadrant.\\
(B) It always diverges.\\
(C) It always converges.\\
(D) none of the above.