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If the vertices of an equilateral triang...

If the vertices of an equilateral triangle be represented by the complex numbers `z_(1),z_(2),z_(3)` on the Argand diagram, then prove that,
`z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).`

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