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If a complex number z satisfies |2z+10+1...

If a complex number `z` satisfies `|2z+10+10 i|lt=5sqrt(3)-5,` then the least principal argument of `z` is

A

`-(5pi)/(6)`

B

`-(11pi)/(12)`

C

`-(3pi)/(4)`

D

`-(2pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A

`|2z+10 + 10i| le(5sqrt(3)-5)`
`rArr |z+ 5+ 5i|le (5sqrt(3)-5)/(2)`
Point B has the least principal argument
Now, `AB =(5sqrt(3)-1)/(2)`
`OA = 5 sqrt(2)`
`therefore /_AOB =(pi)/(12)`
`therefore Arg (z)= (5pi)/(6)`
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