- (a) Determine the roots of the equation
$$z ^ { 6 } = 1$$
giving your answers in the form \(\mathrm { e } ^ { \mathrm { i } \theta }\) where \(0 \leqslant \theta < 2 \pi\)
(b) Show the roots of the equation in part (a) on a single Argand diagram.
(c) Show that
$$( \sqrt { 3 } + i ) ^ { 6 } = - 64$$
(d) Hence, or otherwise, solve the equation
$$z ^ { 6 } + 64 = 0$$
giving your answers in the form \(r \mathrm { e } ^ { \mathrm { i } \theta }\) where \(0 \leqslant \theta < 2 \pi\)