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If z=a+ib satisfies "arg"(-1)="arg"(z+3i...

If `z=a+ib` satisfies `"arg"(-1)="arg"(z+3i)`, then `(a-1):b=`

A

`2:1`

B

`1:3`

C

`-1:3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`"arg"(z-1)="arg"(z+3i)`
`rArr "arg"(a-1)+ib)="arg"(a+(b+i)`
`rArr tan^(-1)b(a-1)=tan^(-1)(b+3)/a`
`rArr ab=(a-1)(b+3)`
`rArr 3(a-1)=b rArr (a-1):b=1:3`
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