PRINT OUT FOR YOUR RECORDS
- Express $\cos 6\theta$ in terms of $\cos^n \theta$
[3 marks]
- Express $\cos^6 \theta$ in terms of $\cos (n\theta)$
[4 marks]
- Solve, giving your answers in the form $re^{i\theta}$ with $ -\pi < \theta \leq \pi$ , \[ z^6=1-\sqrt3 i \]
Represent your solutions on an Argand diagram
[4 marks]
- Represent on an Argand diagram the locus of $z$ s.t.
- $\arg{(z-3-2i)} = -\frac{5\pi}{6}$
[3 marks]
- $|z+1|=|z-2i|$ also give the cartesian equation
[3 marks]
- $|z+1|=|4z-8i|$ also give the cartesian equation
[4 marks]
- Give the cartesian equation and sketch the locus \[ \arg (\frac{z+3}{z-3}) = 3\pi /4 \]
[6 marks]
- $\arg{(z-3-2i)} = -\frac{5\pi}{6}$