[JEE Advanced 1981] z 1 z 2 z 3 are vertices of an equilateral triangle with circumcentre
$z_1,z_2,z_3$ are vertices of an equilateral triangle with circumcentre $z_0$. Prove $z_1^2+z_2^2+z_3^2=3z_0^2$.
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· 2d ago
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Answer: Proved.
For an equilateral triangle $z_1^2+z_2^2+z_3^2=z_1z_2+z_2z_3+z_3z_1$. With $z_0=\frac{z_1+z_2+z_3}3$, $(z_1+z_2+z_3)^2=\sum z^2+2\sum z_iz_j=3\sum z^2$, giving $\sum z^2=3z_0^2$.
JEE Advanced 1981 · Complex Numbers — verified solution by the Vidaara Team.
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