Let such that ,

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

Problem

Let z1,z2,z3∈Cz_1,z_2,z_3\in\mathbb{C} such that ∣z1∣=1\lvert z_1\rvert=1, ∣z2−(1+3i)∣=3\lvert z_2-(1+\sqrt3i)\rvert=3, and ∣z3−3−33i∣=7\lvert z_3-3-3\sqrt3i\rvert=7. If ∣3z1−2z2−4z3∣\lvert3z_1-2z_2-4z_3\rvert is maximum, then the value of ∣z3−z1∣+z3+3z1z2\lvert z_3-z_1\rvert+\frac{z_3+3z_1}{z_2} is

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