9709 P32 - Nov 2017 - Q7
1965
The complex number \(1 - (\sqrt{3})i\) is denoted by \(u\).
(i) Find the modulus and argument of \(u\).
(ii) Show that \(u^3 + 8 = 0\).
(iii) On a sketch of an Argand diagram, shade the region whose points represent complex numbers \(z\) satisfying both the inequalities \(|z - u| \leq 2\) and \(\text{Re } z \geq 2\), where \(\text{Re } z\) denotes the real part of \(z\).
