Question

高中数学问题（复数)

若复数z满足1-z/1+z=i,则|z+1|的值为__________

Answer 1

由已知有 1-z = i(1+z)=i+iz
有(1+i)z=1-i, z = (1-i)/(1+i)
所以z+1 = (1-i)/(1+i)+1 = 2/(1+i)
|z+1| = | 2/(1+i)| =|2|/|1+i|= 2/根号2 = 根号2

Answer 2

1-z=i+iz,
z(i+1)=1-i,
z=1-i/i+1,
z+1=2/i+1=1-i,
|z+1|=2^1/2