De Moivre's theoremAQA A-Level Further Maths: Mind map

Exam questions on De Moivre's theorem

1. The complex number $z=\cos\frac{\pi}{12}+\mathrm{i}\sin\frac{\pi}{12}$.
   Express $z^{-5}$ in the form $\cos\alpha-\mathrm{i}\sin\alpha$, stating the exact value of $\alpha$.2 marks
2. The complex number $w=1+\mathrm{i}$.
   Find $w^{10}$ in the form $a+b\mathrm{i}$.2 marks
3. The equation $8x^3-6x-1=0$ is to be solved.
   Use de Moivre's theorem to show that $\cos3\theta=4\cos^3\theta-3\cos\theta$.3 marks