# A Problem in Complex Numbers!

Algebra Level 4

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 $$z_1\times z_2\times z_3$$.

Note

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

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