If `sqrt(5-12 i)+sqrt(-5-12 i)=z` , then principal value of `a rgz` can be

Options

A. `-(pi)/(4)`
B. `(pi)/(4)`
C. `(3pi)/(4)`
D. `-(3pi)/(4)`

Answer

A, B, C, D

Explanation

`sqrt(5-12i) = sqrt((3-2i)^(2)) = pm (3-2i)`
`sqrt(-5-12i)= sqrt((2-3i)^(2)) = pm (2-3i)`
`rArr z = sqrt(5-12i) + sqrt(5-12i) = sqrt((3-2i)^(2)) = pm (3-2i)`
`sqrt(-5-12i)= sqrt((2-3i)^(2)) = pm (2-3i)`
`rArr z = sqrt(5-12i) + sqrt(-5-12i)`
`=- 1-i, -5 + 5i,5-5i, 1+i`
Therefore, principal values of arg are `- 3pi//4, 3pi//4,-pi//4, pi//4`.