Exponential form of a complex numberAQA A-Level Further Maths: Mind map

Exam questions on Exponential form of a complex number

1. The complex number $z=2\mathrm{e}^{\mathrm{i}\pi/3}$.
   Find $z^3$ in the form $a+b\mathrm{i}$.2 marks
2. The complex numbers $w_1=3\mathrm{e}^{\mathrm{i}\pi/4}$ and $w_2=2\mathrm{e}^{-\mathrm{i}\pi/4}$.
   Express $w_1^2w_2$ in the form $r\mathrm{e}^{\mathrm{i}\theta}$.2 marks
3. The complex number $z=1-\sqrt3\,\mathrm{i}$.
   Express $z$ in the form $r\mathrm{e}^{\mathrm{i}\theta}$, where $r>0$ and $-\pi<\theta\le\pi$.3 marks