The value of  will be:

CONCEPT:

Complex Numbers: For a complex number z = a + ib, the following are defined:

arg(z) = θ = .

Properties of argument:

Let z, z1 and z2 be three complex numbers. Then

1. 

2. arg (z1 ⋅ z2) = arg (z1) + arg (z2)

3. 

4. arg (zn) = n ⋅ arg (z)

5. arg (z1 / z2) = arg (z1) – arg(z2)

6. The argument of zero is not defined

7. If arg (z) = 0 ⇒ z is real

Calculation:

Let,

    ----(1)

∵ arg (z1 / z2) = arg (z1) – arg(z2)

⇒ θ = arg(1 + √3i)(√3 + i) - arg(1 + i) 

∵ arg (z1 ⋅ z2) = arg (z1) + arg (z2)

⇒ θ = arg(1 + √3i) + arg(√3 + i) - arg(1 + i)

Hence, option 3  is correct.