Question 65
Let $z$ be a complex number such that $\arg z \in [\frac{\pi}{2}, \pi]$ and $z^6 + z^3 + 1 = 0$. Determine the modulus and the argument of $z$. The argument of the complex number $z = |z|(\cos\varphi + i\sin\varphi)$ is the number $\arg z = \varphi$.