For a complex number z, arg (z + 1) = π/6 and arg (z – 1) = 2π/3, z is 

1
\(z = \frac{1}{2} + \frac{{\sqrt 3 }}{2}i\)
2
\(z = \frac{1}{2} - \frac{{\sqrt 3 }}{2}i\)
3
\(z = -\frac{1}{2} + \frac{{\sqrt 3 }}{2}i\)
4
\(z = -\frac{1}{2} -\frac{{\sqrt 3 }}{2}i\)

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