已知复数Z满足(1+√3i)Z=1+i,则|Z|等于?
问题描述:
已知复数Z满足(1+√3i)Z=1+i,则|Z|等于?
答
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.