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 z4−|z|4=4iz2, where i=√−1. Then the minimum possible value of |z1−z2|2, where z1,z2∈S with Re(z1)>0 and Re(z2)<0, is

For a complex number z, let Re(z) denote the real part of z. Let S be

1.	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 z4−\|z\|4=4iz2, where i=√−1. Then the minimum possible value of \|z1−z2\|2, where z1,z2∈S with Re(z1)>0 and Re(z2)<0, is
Answer» 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 $z^{4} - {\| z \|}^{4} = 4 i z^{2},$ where $i = \sqrt{- 1} .$ Then the minimum possible value of ${\| z_{1} - z_{2} \|}_{1}^{2},$ where $z_{1}, z_{2} \in S$ with $Re (z_{1}) > 0$ and $Re (z_{2}) < 0,$ is