Question

若复数z满足

1-z

1+z

=i，则|z+1|的值为______．

Answer 1

∵复数z满足

1-z

1+z

=i，解得 z=

1-i

1+i

=

(1-i)(1-i)

(1+i)(1-i)

=

-2i

2

=-i，
∴z+1=1-i，∴|z+1|=

1+1

=

2

，
故答案为

2

．