Paragraph for Question 7 & 8

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

Problem

Paragraph for Question 7 & 8. On the argand plane consider A(z1)A(z_1) , B(z2)B(z_2) and C(z3)C(z_3) as distinct complex numbers lying on the curve ∣z∣=3|z| = \sqrt{3} . If △ABC\triangle ABC is equilateral and P(zp)P(z_p) being a point such that ∣z1∣=∣zp∣|z_1| = |z_p| , then the value of ∣zp−z1∣2+∣zp−z2∣2+∣zp−z3∣2|z_p - z_1|^2 + |z_p - z_2|^2 + |z_p - z_3|^2 is

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