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For a complex number z ,let Re(z) denote...

For a complex number `z` ,let `Re(z)` denote the real part of `z` . Let `S` be the set of all complex numbers `z` satisfying `z^(4)-|z|^(4)=4iz^(2)` ,where `i=sqrt(-1)` . Then the minimum possible value of `|z_(1)-z_(2)|^(2)` ,where, `z_(1),z_(2) in S` with `Re(z_(1))>0` and `Re(z_(2))<0,` is

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