Write $z=re^{i\theta}$ with $-\pi<\theta\leq\pi$. Its principal sixth root is $r^{1/6}e^{i\theta/6}$, whose <complex argument> lies in $(-\pi/6,\pi/6]$. Equality with $2e^{i\pi/6}$ forces $r=64$ and $\theta=\pi$, so \b[$z=-64$].

Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 1 / 1C / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ia/paper-1/1c/ii/solution