Roots of complex numbers and roots of unityAQA A-Level Further Maths: Mind map

Exam questions on Roots of complex numbers and roots of unity

1. The equation $z^6=1$.
   Write down all six roots in the form $\mathrm{e}^{\mathrm{i}\theta}$ with $-\pi<\theta\le\pi$.2 marks
2. The complex number $w=-8$.
   Find the three cube roots of $w$ in the form $a+b\mathrm{i}$.2 marks
3. The equation $z^4=-8+8\sqrt3\,\mathrm{i}$.
   Find the modulus and the arguments, in the range $-\pi<\theta\le\pi$, of the four roots of the equation.3 marks