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 = - 1 . Then the minimum possible value of z 1 - z 2 2 , where z 1 , z 2 ∈ S with Re z 1 > 0 and Re z 2 < 0 , is _______

Step-by-step solution

z 4 - | z | 4 = 4 i z 2 ⇒ z 4 - z z ¯ 2 = 4 i z 2 ⇒    z 2 z 2 - z ¯ 2 = 4 i z 2    ⇒    z 2 - z ¯ 2 = 4 i ⇒    z + z ¯ z - z ¯ = 4 i ⇒    z + z ¯ 2 z - z ¯ 2 i = 1    ⇒    x y = 1 for z 1   &   z 2    ⇒    x 1 y 1 = 1 and x 2 y 2 = 1 x 1   &   x 2 are of opposite sign, similarly y 1 & y 2 are of opposite sign ⇒ &#160