If a complex number $$z = {{\sqrt 3 } \over 2} + i{1 \over 2}$$ then z⁴ is

The function $$$w = u + iv = {1 \over 2}\log \left( {{x^2} + {y^2}} \right) + i{\tan ^{ - 1}}\left( {{y \over x}} \right)$$$ is not analytic at the point.