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May 22, 2019

Triangle in complex plane - ISI 2019 Obj P8

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Understand the problem

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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

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Complex Numbers and Geometry

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6 out of 10

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Complex Numbers from A to Z by Titu Andreescu

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Start with hints

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Do you really need a hint? Try it first!

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Connected Program at Cheenta

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Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.

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Similar Problem

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