z1+z2+z3=3z0(z1+z2+z3)2=9z02⇒z12+z22+z32+2(z12+z22+z32)=9z02⇒z12+z22+z32=3z62
k=1∑3(zk−z0)2=(z1−z0)2+(z2−z0)2+(z3−z0)2=z12+z22+z32+3z02−2(z1+z2+z3)z0=6z02−6z02=0
If z_1, z_2, z_3 ∈ C are the vertices of an equilateral triangle, whose centroid is z_0, then Σ_ k=1^3 ( z_ k- z_0 )^2 is equal to
JEE Main 2025 — Mathematics Algebra
2025mcqmedium
If z1,z2,z3∈C are the vertices of an equilateral triangle, whose centroid is z0, then k=1∑3(zk−z0)2 is equal to
Official previous-year question
Held on 3 Apr 2025 · Verified 6 Jul 2026.
Options
- A
0
- B
1
- C
i
- D
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