The number of complex numbers satisfying z¯=iz2 is

|z¯|=iz2⇒|z|=|z|2⇒          |z|=0  or  |z|=1.If |z|=0, then  z=0If |z|=1, we get ⁡z¯=1/z so that the equation becomes  1/z=iz2or                                z3=−i=i3⇒z=i,iω,iω2where ω(≠1) ) is a cube root of unity