A Problem in Complex Numbers!

Algebra Level 5

Let \(z_1,z_2,z_3\) be 3 complex numbers lying on a circle whose centre is at the origin such that \(z_i+z_{j}z_k\) (where \(i,j,k\in \{1,2,3\}\) and \(i \ne j \ne k\)) are real numbers, then find \(z_1\times z_2\times z_3\).


  • \(z_1\ne z_2\ne z_3\). In other words, \(z_1,z_2,z_3\) are all distinct points on the circle.

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