3. (a) Solve the following equation, where X is a 2 × 2-matrix:
$\begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix} X \begin{pmatrix} -1 & 1 \ 0 & 2 \end{pmatrix} = \begin{pmatrix} 3 & 2 \ -1 & 0 \end{pmatrix}$.
[4 marks].
(b) State De Moivre's formula, and use it to find integers A and B such that
sin 3$\theta$ = A sin³$\theta$ + B sin $\theta$.
[3 marks]
(c) Calculate $(-1 - i\sqrt{3})^4$, writing your answer in the form a + bi. Plot your answer in an
Argand diagram
[3 marks]
