The roots of $ z $ are:
$$ \sqrt{z} = 1.0824-2.6131i $$ $$ \sqrt{z} = -1.0824+2.6131i $$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 = -4 \sqrt{ 2 } $ and $ b = -4 \sqrt{ 2 } $ )