[JEE Advanced 1983] prove that z 1 z 2 and the origin form an equilateral triangle only
Prove that $z_1,z_2$ and the origin form an equilateral triangle only if $z_1^2+z_2^2-z_1z_2=0$.
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· 2d ago
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Answer: Proved.
Equilateral with the origin requires $z_2=z_1e^{\pm i\pi/3}$. Then $z_1^2+z_2^2-z_1z_2=z_1^2(1+e^{\pm2i\pi/3}-e^{\pm i\pi/3})=0$ since $1-e^{i\pi/3}+e^{2i\pi/3}=0$.
JEE Advanced 1983 · Complex Numbers — verified solution by the Vidaara Team.
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