已知复数z=(根号3+i)/(1-根号3i)^2,则|z|=______
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解决时间 2021-04-02 02:31
- 提问者网友：城市野鹿
- 2021-04-01 06:28
已知复数z=(根号3+i)/(1-根号3i)^2,则|z|=______
最佳答案
- 五星知识达人网友：轻雾山林
- 2021-04-01 06:53
z=(√3+i)/(1-√3i)^2
=(√3+i)/(1-2√3i+3i^2)
=(√3+i)/(-2-2√3i)
=(√3+i)/(-2)(1+√3i)
=(√3+i)(1-√3i)/(-2)(1+√3i)(1-√3i)
=(√3-3i+i-√3i^2)/(-2)(1-3i^2)
=(2√3-2i)/(-2)(4)
=-√3/4 +i/4
|z|=√[(-√3/4)^2+(1/4)^2]
=√(3/16+1/16)
=√1/4
=1/2
=(√3+i)/(1-2√3i+3i^2)
=(√3+i)/(-2-2√3i)
=(√3+i)/(-2)(1+√3i)
=(√3+i)(1-√3i)/(-2)(1+√3i)(1-√3i)
=(√3-3i+i-√3i^2)/(-2)(1-3i^2)
=(2√3-2i)/(-2)(4)
=-√3/4 +i/4
|z|=√[(-√3/4)^2+(1/4)^2]
=√(3/16+1/16)
=√1/4
=1/2
全部回答
- 1楼网友：春色三分
- 2021-04-01 07:38
- 2楼网友：神也偏爱
- 2021-04-01 07:20
已知复数z=(根号3+i)/(1-根号3i)^2,则|z|=___1/4___
z=(根号3+i)/(1-根号3i)^2
=(根号3+i)/(-2-2根号3i)
=-i/4
z=(根号3+i)/(1-根号3i)^2
=(根号3+i)/(-2-2根号3i)
=-i/4
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