1. （5 分）设复数 $z$ 满足 $\frac{1+z}{1-z}=i$, 则 $|z|=(\quad)$
Gaokao · Math · previous-year question
- A.1correct
- B.$\sqrt{2}$
- C.$\sqrt{3}$
- D.2
Answer
A. 1
Explanation
解: $\because$ 复数 $z$ 满足 $\frac{1+z}{1-z}=i$, $\therefore 1+z=i-z i$, $\therefore z(1+i)=i-1$, $\therefore z=\frac{i-1}{i+1}=i$ $\therefore|z|=1$ 故选: A.
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