Let be the set of all complex numbers satisfying

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

Problem

Let SS be the set of all complex numbers zz satisfying z4−∣z∣4=4iz2z^4-|z|^4=4iz^2. Then find the minimum possible value of ∣z1−z2∣2|z_1-z_2|^2, where z1,z2∈Sz_1,z_2\in S, Re⁡(z1)>0\operatorname{Re}(z_1)>0, and Re⁡(z2)<0\operatorname{Re}(z_2)<0.

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