### Problem with complex numbers

Posted:

**Thu Mar 01, 2018 3:39 pm**Let be $z_1,z_2,z_3 \in \mathbb{C}$ such that $z_1+z_2+z_3=z_1^7+z_2^7+z_3^7=0.$ Prove that: $|z_1|=|z_2|=|z_3|.$

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Posted: **Thu Mar 01, 2018 3:39 pm**

Let be $z_1,z_2,z_3 \in \mathbb{C}$ such that $z_1+z_2+z_3=z_1^7+z_2^7+z_3^7=0.$ Prove that: $|z_1|=|z_2|=|z_3|.$