Rotation Theorem

JEE Main Mathematics · Complex Numbers · 3 questions, latest first

• 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 to20253 April, Shift 2 · Q5
• Let O be the origin, the point A be z_1=√3+2 √2 i, the point B(z_2) be such that √3|z_2|=|z_1| and (z_2)= (z_1)+(π)/6. Then202528 January, Shift 1 · Q3
• Let w_1 be the point obtained by the rotation of z_1=5+4 i about the origin through a right angle in the anticlockwise direction,…202311 April, Shift 1 · Q14