If Z₁,Z₂,Z₃ are vertices of an equilateral triangle with |Z₁|=|Z₂|=|Z₃|, then Z₁+Z₂+Z₃=0.

Answer: True. Equal moduli put the circumcentre at the origin; for an equilateral triangle the centroid coincides with it, so Z₁+Z₂+Z₃=3·0=0. JEE Advanced 1984 · Complex Numbers — verified solution by the Vidaara Team.

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[JEE Advanced 1984] if z 1 z 2 z 3 are vertices of an equilateral triangle with

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If $Z_1,Z_2,Z_3$ are vertices of an equilateral triangle with $|Z_1|=|Z_2|=|Z_3|$, then $Z_1+Z_2+Z_3=0$.

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VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Answer: True.

Equal moduli put the circumcentre at the origin; for an equilateral triangle the centroid coincides with it, so $Z_1+Z_2+Z_3=3\cdot0=0$.

JEE Advanced 1984 · Complex Numbers — verified solution by the Vidaara Team.

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