Factor a cubic and choose exact principal arguments

Do not use a calculator.

(a) Show that $z=2i$ is a root of $z^3+2z+4i=0$. 2 marks Hence find the other roots.3 marks

(b) Given $w_1=-1-i$ and $w_2=-\dfrac{\sqrt6}{2}+\dfrac{\sqrt2}{2}i$, find their moduli and arguments exactly.2 marks