已知复数z=(根号3+i)/(1-根号3i)^2,则|z|=__

发布网友 发布时间：2024-09-30 16:01

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热心网友 时间：2024-10-07 08:05

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

热心网友 时间：2024-10-07 07:58

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

热心网友 时间：2024-10-07 08:04

热心网友 时间：2024-10-07 08:02

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

热心网友 时间：2024-10-07 08:01

热心网友 时间：2024-10-07 08:03

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