The correct options are
A √32+√32i
B √32−√32i
C −√32+√32i
D −√32−√32i
Let z=x+iy
⇒z2=x2−y2+2ixy
⇒Re(z2)=x2−y2=0 ⋯(1)
Also, |z|=√x2+y2=√3
⇒x2+y2=3 ⋯(2)
Solving equation (1) and (2), we get
x=±√32,y=±√32⇒z=√32+√32i, √32−√32i, −√32+√32i, −√32−√32i
Thus, there are four complex numbers.