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

Source of the problem



Complex Numbers and Geometry

Difficulty Level

6 out of 10

Suggested Book

Complex Numbers from A to Z by Titu Andreescu

Start with hints

Do you really need a hint? Try it first!

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