Express $u$ in the form $r(\cos\theta+i\sin\theta)$ where $r>0$ and $0\leq\theta<2\pi$

Hence, or otherwise, determine both square roots of $u$ giving your answers in the form $a+bi$

A polynomial with real coefficients has $2+2\sqrt{3}\,i$ as a root. State the other root in its conjugate pair and hence determine the monic quadratic factor associated with this pair.