Find the roots of $z^2 + (2\sqrt{3})z + 4 = 0$, and give the answers in the form $x + iy$, where $x$ and $y$ are real.
(ii)[3]
State the modulus together with the argument of each root.
(iii)[3]
With all working shown, confirm that each root also satisfies $z^6 = -64$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the quadratic formula, completing the square, or the substitution $z=x+iy$ to obtain a root, and use $i^2=-1$” …