[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by KS. More of him can be found here.

(i) Find the two possible values of $z$ such that $z^2 = 1 + \sqrt{3}i$, leaving your answer in exact form $a + bi$, where $a$ and $b$ are real numbers.

(ii) Hence or otherwise, find the exact roots of the equation

$2w^2 + 2 \sqrt{6}w + 1 - 2 \sqrt{3} i = 0$