已知复数Z满足(1+√3i)Z=1+i,则|Z|等于?

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已知复数Z满足(1+√3i)Z=1+i,则|Z|等于?已知复数Z满足(1+√3i)Z=1+i,则|Z|等于?已知复数Z满足(1+√3i)Z=1+i,则|Z|等于?z(1+√3i)=1+i所以z=(1+

已知复数Z满足(1+√3i)Z=1+i,则|Z|等于?
已知复数Z满足(1+√3i)Z=1+i,则|Z|等于?

已知复数Z满足(1+√3i)Z=1+i,则|Z|等于?
z(1+√3i)=1+i
所以z=(1+i)/(1+√3i)
=(1+i)(1-√3i)/[(1+√3i)(1-√3i)]
=[(1+√3)+(1-√3)i]/4
|z|=√[(1+√3)²+(1-√3)²]/4
=2√2/4
=√2/2.