Let Z and Z1 be conjugate complex numbers, and (Z + z1) & sup2; - 3Z * z1i = 4-6i Finding complex numbers Z and Z1

Let Z and Z1 be conjugate complex numbers, and (Z + z1) & sup2; - 3Z * z1i = 4-6i Finding complex numbers Z and Z1

z=a+bi
z1=a-bi
a. B is a real number
So Z + Z1 = 2A
z*z1=a^2+b^2
So 4A ^ 2 - (3a ^ 2 + 3B ^ 2) I = 4-6i
4a^2=4
3a^2+3b^2=6
a^2=1
b^2=1
therefore
z=1+i,z1=1-i
z=1-i,z1=1+i
z=-1+i,z1=-1-i
z=-1-i,z1=-1+i