If z₁, z₂, z₃ are the vertices of an equilateral triangle whose centroid is z₀, then Σ k=1 ³ (z k - z₀)² is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q64

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

z_1, z_2, z_3\in\mathbb{C}

are the vertices of an equilateral triangle whose centroid is

z_0

, then

\displaystyle\sum_{k=1}^3 (z_k - z_0)^2

is equal to:

JEE Main 2025 · April, Unspecified (session-level dataset) · Q64

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

z_1, z_2, z_3\in\mathbb{C}

are the vertices of an equilateral triangle whose centroid is

z_0

, then

\displaystyle\sum_{k=1}^3 (z_k - z_0)^2

is equal to: