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Prove that the area of the triagle only ...

Prove that the area of the triagle only if `z_1^2+z_2^2+z_3^2=3 z_0^2`

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Since , `z_(1) , z_(2)` and origin form an equilateral triangle .
[`because ` if `z_(1) , z_(2) , z_(3)` from an equilateral triangle , then `z_(1)^(3) + z_(2)^(2) + z_(3)^(2) = z_(1) z_(2) + z_(2)z_(3) + z_(3)z_(1)`]
`implies z_(1)^(2) + z_(2)^(2) + 0^(2) = z_(1)z_(2) + z_(2)*0 + 0*z_(1)`
`implies z_(1)^(2) + z_(2)^(2) = z_(1)z_(2)`
`implies z_(1)^(2) + z_(2)^(2) - z_(1)z_(2) = 0`
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