Let and be two complex numbers such that and

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

Problem

Let z1z_1 and z2z_2 be two complex numbers such that ∣z2∣=1|z_2| = 1 and z1−1z1+1=(z2−1z2+1)2\frac{z_1 - 1}{z_1 + 1} = \left( \frac{z_2 - 1}{z_2 + 1} \right)^2, then the maximum value of ∣z1−1∣+∣z1+1∣|z_1 - 1| + |z_1 + 1| is - - - .

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