设z,z1为共轭复数,且（z+z1）²-3z*z1i=4-6i求复数z和z1

设z,z1为共轭复数,且（z+z1）²-3z*z1i=4-6i求复数z和z1
设z,z1为共轭复数,且（z+z1）²-3z*z1i=4-6i
求复数z和z1

设z,z1为共轭复数,且（z+z1）²-3z*z1i=4-6i求复数z和z1
z=a+bi
z1=a-bi
a,b是实数
所以z+z1=2a
z*z1=a^2+b^2
所以4a^2-(3a^2+3b^2)i=4-6i
4a^2=4
3a^2+3b^2=6
a^2=1
b^2=1
所以
z=1+i,z1=1-i
z=1-i,z1=1+i
z=-1+i,z1=-1-i
z=-1-i,z1=-1+i