Question

已知复数z₀=2+i，复数z满足zz₀=z+z₀，则复数z=______．

Answer 1

复数z₀=2+i，复数z满足zz₀=z+z₀，所以z=

2+i

1+i

=

(2+i)(1-i)

(1+i)(1-i)

=

3-i

2

=

3

2

-

1

2

i．
故答案为：

3

2

-

1

2

i