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Let z be a complex number satisfying |z+...

Let `z` be a complex number satisfying `|z+16|=4|z+1|`. Then

A

`|z|=4`

B

`|z|=5`

C

`|z|=6`

D

`3 lt |z| lt68`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `|z+16|^(2)=16|z+1|^(2)`
`implies (z+16)(barz+16)=16(z+1)(barz+1)`
`implieszbarz+16z+16barz+256=16zbarz+16z+16barz+16`
`implieszbarz=16implies|z|^(2)=16implies|z|=4`
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