The roots of $ z $ are:
$$ \sqrt{z} = \frac{\sqrt{ 3 }}{ 2 }-\frac{ 1 }{ 2 }i $$ $$ \sqrt{z} = - \frac{\sqrt{ 3 }}{ 2 }+\frac{ 1 }{ 2 }i $$The square roots of $ z = a + bi $ are:
$$ z_1 = \alpha + \beta i ~~~\text{ and }~~~ z_2 = -\alpha - \beta i $$where:
$$ \alpha = \sqrt{\frac{a + \sqrt{a^2 + b^2}}{2}} ~~~\text{ and }~~~ \beta = sgn(b) \sqrt{\frac{-a + \sqrt{a^2 + b^2}}{2}} $$( In this example we have $ a = \frac{ 1 }{ 2 } $ and $ b = - \frac{\sqrt{ 3 }}{ 2 } $ )