Find all non zero complex numbers z satisfying `barz=iz^2`

Find the non-zero complex numbers z satisfying z=iz^(2)

Find all complex numbers satisfying barz = z^2 .

Find all complex number z satisfying bar(z)+1=iz^(2)+|z|^(2)

Find number of all complex numbers z satisfying bar(z) =iz^2

The nonzero complex number Z satisfying Z=iZ^(2) is

Modulus of nonzero complex number z satifying barz + z =0 and |z|^(2)-4iz=z^(2) is _____.

Let z_(1),z_(2) and z_(3) be non-zero complex numbers satisfying z^(2)=bar(iz), where i=sqrt(-1). What is z_(1)+z_(2)+z_(3) equal to ?