Roots of complex numbersEdexcel International A Level Further Maths: Mind map

Exam questions on Roots of complex numbers

1. Consider the equation $z^3=8$.
   Find the non-real roots of the equation in the form $a+ib$, giving $a$ and $b$ as exact values.2 marks
2. The complex number $w=-8+8\sqrt3\,i$ and the equation $z^4=w$.
   Find the four roots of $z^4=w$ in the form $re^{i\theta}$, where $-\pi<\theta\le\pi$.2 marks
3. Consider the equation $z^3=-27i$.
   Solve the equation, giving the roots in the form $re^{i\theta}$, where $-\pi<\theta\le\pi$.3 marks