Complex numbers - set notation

How to express in set notation $A\setminus B$, where :

$$A = \{Z \text{ is an element of complex no.s such that } z^6 = 1-i\sqrt3 \}$$

$$B = \{ Z \text{ is an element of complex no.s such that }\Im(z) > 1/2 \}$$

HINT: one way to write the notation is solving the angles that makes the imaginary part of $z$ less or equal than $1/2$, that is, the equation $$z^6=1-i\sqrt 3$$

have six solutions for each $z$, you must choose the solutions for when $\Im(z)\le 1/2$. This imply that it must hold that

$$\sin\alpha\le 1/2$$

where $\alpha$ is the argument of $z$. This means that $\alpha\notin(\pi/6,5\pi/6)$. With this information we can write an explicit definition for $A\setminus B$ in terms of the argument of $z$ and it modulus.

Or if you dont want to make the definition explicit we can write simply

$$A\setminus B=\{z\in\Bbb C:z^6=1-i\sqrt3\;\land\;\arg(z)\notin(\pi/6,5\pi/6)\}$$

or

$$A\setminus B=\{z\in\Bbb C:z^6=1-i\sqrt3\;\land\;\Im(z)\le 1/2\}$$