If `a` complex number `z` satisfies `|2z+10+10i| le 5sqrt3-5,` then the least principal argument of `z` is : (a) `-(5pi)/6` (b) `(11pi)/12` (c) `-(3pi)/4` (d) `-(2pi)/3`

Options

A. `-(5pi)/(6)`
B. `-(11pi)/(12)`
C. `-(3pi)/(4)`
D. `-(2pi)/(3)`

Answer

A

Explanation

`|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)`