Suppose we have 3 complex numbers , such that $$|z_1|=|z_2|=|z_3|=1$$ and they form equilateral triangle then will condition $$z_1.z_2.z_3=1$$ always be true? I know cube roots of unity , that is $w,w^2,1$ satisfy here but is this always true?
2026-05-02 14:53:02.1777733582
Complex number forming equilateral triangle
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No. Rotate the three point by multiplying with $e^{i\theta}$. Then the product is multiplied by $e^{3i\theta}$.