If z1,z2 and z3 are complex numbers such...

If `z_1,z_2 and z_3` are complex numbers such that `|z_1|=|z_2|=|z_3|= |1/z_1+1/z_2+1/z_3|=1, then |z_1+z_2+z_3|` is

equal to 1

less than 1

greater than 3

equal to 3

Text Solution

Verified by Experts

The correct Answer is:

Given `" "|z_1|=|z_2|=|z_3|=1`
Now `" "|z_1|=1`
`rArr " " |z_1|^2=1 rArr z_1 bar z_1=1`
similarly `z_2barz_2=1,z_3 bar z_3=1`
Again Now `" "|1/z_1+1/z_2+1/z_3|=1`
`rArr |barz_1+barx_2+bar3 |=1rArr |z_1+z_2+z_3=1`
`rArr " "|z_1+z_2+z_3|=1`

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