Let ~~let~~ be complex numbers of equal magnitude satisfying and

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let let z1,z2,z3z_1, z_2, z_3 be complex numbers of equal magnitude satisfying z1+z2+z3=−32−i5z_1 + z_2 + z_3 = -\frac{\sqrt{3}}{2} - i\sqrt{5} and z1⋅z2⋅z3=3+i5z_1 \cdot z_2 \cdot z_3 = \sqrt{3} + i\sqrt{5} . If z1=x1+iy1,z2=x2+iy2z_1 = x_1 + i y_1, z_2 = x_2 + i y_2 and z3=x3+iy3;x1,x2,x3,y1,y2,y3∈Rz_3 = x_3 + i y_3; x_1, x_2, x_3, y_1, y_2, y_3 \in \mathbb{R} , where i=−1i = \sqrt{-1} , then 16(x1y1+x2y2+x3y3)25=?\frac{16(x_1 y_1 + x_2 y_2 + x_3 y_3)^2}{5} = ?

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