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# Understand the problem

For each natural number k, choose a complex number $z_k$ , with$| z_k | = 1$, and denote $a_k$ by the area of the triangle formed by $z_k , i \cdot z_k , z_k + i \cdot z_k$ . Then which of the following is true for the series below:  $$\Sigma (a_k)^k$$

(1) It converges only if every $z_k$ lies in the same quadrant
(2) It always diverges
(3) It always converges
(4) None of the above

##### Topic

Complex Numbers and Geometry

6 out of 10

##### Suggested Book

Complex Numbers from A to Z by Titu Andreescu

Do you really need a hint? Try it first!

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