Question

若复数z1,z2,z3满足|z1|=|z2|=|z3|=√2,则|(z1+z2+z3)/1/z1+1/z2+1/z3|=

Answer 1

1/z1+1/z2+1/z3

=(z1.z2+z2.z3+z3.z1)/(z1.z2.z3)

(z1+z2+z3)/[1/z1+1/z2+1/z3]

=(z1+z2+z3).(z1.z2.z3)/(z1.z2+z2.z3+z3.z1)

=(|z1|^2.z2.z3+|z2|^2.z3.z1+|z3|^2.z1.z2 )/(z1.z2+z2.z3+z3.z1)

=2(z1.z2+z2.z3+z3.z1)/(z1.z2+z2.z3+z3.z1)

=2

|(z1+z2+z3)/[1/z1+1/z2+1/z3]|=2