复数x0=3+2i,复数z满足z*z0 =3z+z0,则复数z=_数学解答

复数x0=3+2i,复数z满足z*z0 =3z+z0,则复数z=

人气：314 ℃　时间：2020-04-23 12:07:02

解答

z=a+bi
(a+bi)(3+2i)=3(a+bi)+3+2i
(3a-2b)+(2a+3b)i=(3a+3)+(3b+2)i
所以
3a-2b=3a+3
2a+3b=3b+2
b=-3/2,a=1
所以z=1-3i/2